DATE LABEL
THE
INTERNATIONAL SERIES
OF
MONOGRAPHS ON PHYSICS
GENERAL EDITORS
N. F. MOTT E. C. BULLARD
THE INTERNATIONAL SERIES OF
MONOGRAPHS ON PHYSICS
GENERAL EDITORS
N. F. MOTT
Cavendish Professor of Physics
in the University of
Cambridge
E. C. BULLARD
Direotor of the National
Physical Laboratory
Teddington
Already Published
THE THEORY OF ELECTRIC AND MAGNETIC SUSCEPTIBILITIES.
By J. b. VAN vleck. 1932.
THE THEORY OF ATOMIC COLLISIONS. By n. f. mott and h. s. w.
massey. Second edUion. 1949.
RELATIVITY. THERMODYNAMICS. AND COSMOLOGY. By b. o. tol-
MAN. 1934.
KINEMATIC RELATIVITY. A sequel to Relativity. Gravitation, and World-
Structure. By E. A. MILNE. 1948.
THE PRINCIPLES OF STATISTICAL MECHANICS. By b. c. tolman. 1938.
ELECTRONIC PROCESSES IN IONIC CRYSTALS. By n. f. mott and
B. w. oubney. Second edition. 1948.
GEOMAGNETISM. By s. chapman and J. bartels. 1940. 2 vols.
THE SEPARATION OF GASES. By m. ruhemann. Second edition. 1949.
THE PRINCIPLES OF QUANTUM MECHANICS. By p. a. m. dibao.
Third edition. 1947.
THEORY OF ATOMIC NUCLEUS AND NUCLEAR ENERGY SOURCES.
By o. oamow and c. l. cbitchfield. 1949. Being the third edition of struc¬
ture of ATOMIC nucleus and nuclear transformations.
THE PULSATION THEORY OF VARIABLE STARS. By s. bosseland.
1949.
THEORY OF PROBABILITY. By harold Jeffreys. Second edition. 1948.
RADIATIVE TRANSFER. By 8. chandraseehab. 1960.
COSMICAL ELECTRODYNAMICS. By h. alfvAn. 1950.
COSMIC RAYS. By l. jAnossy. Second edition. 1950.
THE FRICTION AND LUBRICATION OF SOLIDS. By f. p. bowden and
D. TABOR. 1950.
ELECTRONIC AND IONIC IMPACT PHENOMENA. By h. s. w. massey
and e. h. 8. burhop. 1952.
THE THEORY OF RELATIVITY. By c. moller. 1952.
MIXTURES. By e. a. ocooenhetm. 1952.
BASIC METHODS IN TRANSFER PROBLEMS. By v. kouroanoff with
the collaboration of n>A w. busbridoe. 1952.
THE OUTER LAYERS OF A STAR. By b. v. d. b. woolley and d. w. h. stibbs.
1963.
DISLOCATIONS AND PLASTIC FLOW IN CRYSTALS. By a. h. cottbell.
1953.
ELECTRICAL BREAKDOWN OF OASES. By J. m. meek and j. d. cbaoos.
1953.
GEOCHEMISTRY. By the late v. m. Goldschmidt. Edited by alex muir.
1954.
THE QUANTUM THEORY OF RADIATION. By w. heitler. Third edition.
1954.
ON THE ORIGIN OF THE SOLAR SYSTEM. By h. alfv£n. 1954.
DYNAMICAL THEORY OF CRYSTAL LATTICES. By m. born and
k. huano. 1954.
METEOR
ASTRONOMY
BY
A. C. B. LOVELL
OXFORD
AT THE CLARENDON PRESS
1954
Oxford University Press, Amen House, London E.C.4
„„„ NEW YORK TORONTO MELBOURNE wttLKOTOK
BOMBAY CALCOTTA -ABBAS KABACH, CABK TO- »AOAB
Geoffrey Cumberkge, Publisher to the UmversUy
PRINTED IN OREAT B
v>" & N
V V * 3 • 5"b
L 943<*?\W
UBRORt
PREFACE
It is now twenty-seven years since the publication of the last compre¬
hensive book on meteors. Recently the study of meteors has been trans¬
formed by the new photographic and radio-echo techmques and a
modern treatment of the subject has become very desirable. When the
present monograph was planned in 1949 it was intended to cover^the
entire field of meteors. However, it soon became evident that it would
be impossible to compile such a work in any reasonable time, or in a
single volume. With the publication of the present book, which deals
only with the astronomy of meteors, the task is only half complete. A
further volume, dealing with meteor physics, will be necessary to com¬
plete the original scheme and it is hoped that it may be possi >le to
compile this at some future date.
In writing this book I have received much assistance from my col¬
leagues working on meteors at Jodrell Bank. I am greatly indebted to
Dr. J. G. Davies and Dr. G. S. Hawkins whose work, much of it still
unpublished, forms the basis of certain sections of the book. I also wish
to thank particularly, Prof. Z. Kopal, Mr. J. P. M. Prentice, Dr. Davies,
Dr. Hawkins, and Miss M. Almond who have read and criticized the
manuscript. The original for Plate I, and permission to reproduce, was
kindly supplied by Dr. D. W. R. McKinley. The photograph for Plate II
was taken by Mr. S. Evans of Jodrell Bank.
J A C. R T,.
UNIVERSITY OF MANCHESTER
JODRELL BANK EXPERIMENTAL STATION
LOWER WITHINOTON
CHESHIRE
December, 1952
CONTENTS
l
I. Introduction
II. Observational Methods
i. Visual and Photographic Techniques
III. Observational Methods
ii. The History and Fundamental Features of Radio-echo
Observations
IV. Observational Methods
ra. Radio-echo Techniques for the Measurement of Meteor
Radiants and Velocities
V. The Fundamental Equations of Meteoric Motion
VI. The Diurnal and Seasonal Distribution of Sporadic
Meteors 96
VII. The Number and Mass Distribution of Sporadic Meteors 123
VIII. The Velocity of Sporadic Meteors
i. The von Nicssl-Hoffmeister Fireball Catalogue
IX. The Velocity of Sporadic Meteors
ii. The Work of Opik
X. The Velocity of Sporadic Meteors
ra. Porter’s Analysis of the British Meteor Data
141
155
190
XI. The Velocity of Sporadic Meteors 198
iv. Photographic Results
XII. The Velocity of Sporadic Meteors 212
v. The Radio-echo Results and General Conclusion
XIII. The Major Meteor Showers 248
I. The Permanent Streams of January to June
XIV. The Major Meteor Showers 270
ii. The Permanent Streams of July and August
XV. The Major Meteor Showers
in. The Permanent Streams of September to December
288
CONTENTS
viii
XVI. The Major Meteor Showers 326
iv. The Periodic Streams
XVII. The Major Meteor Showers 349
v. The Lost Streams
XVIII. The Major Meteor Showers 358
vi. The Day-time Streams
XIX. The Number and Mass Distribution of the Shower
Meteors 384
XX. The Dispersive Effects in Meteor Streams 397
XXI. Cosmological Relationships of Meteors 413
Appendix I 435
Appendix II 438
Author Index 446
Subject Index 448
LIST OF TABLES
1. Correction to Zenithal Magnitude page ®
2. Relation between Observational Error e and Magnitude in according to
Opik
3. Limiting Meteor Magnitude Visible at a given Angle from an Observer s
Line of Vision
4. Numbers of Meteors of Different Magnitudes seen by a Visual Observer
6. Displacement of the Beginning and End Points for Common Meteors
with Unequal Recorded Lengths in the Reticule Observations
6. Characteristics of the Harvard Cameras not Specifically Employed for
Moteor Photography
7. Characteristics and Performance of the Meteor Camoras
8. Field Correction for the Harvard AI and FA Camoras
9. Data on a Single Meteor obtained in the 3-Station Radio Measurements
of McKinloy and Mi liman
10. Correction in Minutes of Time to be applied to Timo of Transit for
Various Heights of Moteor Showers
11. Correction Factors in Hoffmeister’s Analysis
12. Probabilities of Telescopic Observations for Various Values of L/D
13. Effective Field of View for Different Moteor Magnitudes
14. Numbor of Motcoro as a Function of Field of View and Magnitude
15. Path Length of Meteors as a Function of Magnitude
16. Correlation of Naked-eye and Telescopic Magnitude Scales
17. Path Length and Effective Area of Visibility for Meteors of Different
Magnitudes
18. Number of Meteors of Different Magnitudes
19. Numbers of Meteors of Different Magnitudes entering the Earth’s
Atmosphoro per Day
20. Froquoncy of Meteors as a Function of Magnitude in Williams’s Analysis 134
21. Comparison of Observed and Computed Meteor Frequencies as a
Function of Magnitude in Williams’s Analysis
22. Relation of Meteor Magnitude and Mass
23. Daily Mass of Sporadic Meteors intercepted by the Earth as a Function
of Meteor Magnitude
24. Mass and Energy brought into the Earth’s Atmosphere by Sporadic
Meteors
9
10
11
15
20
22
54
69
105
126
127
127
128
128
129
130
130
135
137
25. Space Distribution of Sporadic Meteor Material
26. Velocities in Fireball Catalogue for certain Radiant Clusters treated by
Fisher
27. Comparison of Velocities of Meteors belonging to known Showers
compared with the Values given in the Fireball Catalogue
137
138
139
146
150
X
LIST OF TABLES
28. Watson's Analysis of the Distribution in Latitude of Velocity Groups
in the Fireball Catalogue
29. Results of Watson’s Test of the Significance of Apparent Radiant
Groups in the Fireball Catalogue
30. Comparison of Concentration of Meteors in the Arizona Results with
those in the Fireball Catalogue
31. Opik’s Preliminary Grouping of 64 Stream Meteors
32. Corrections required to Angular Velocities in the Rockmg-nurror
Observations
33. Relative Weights to be assessed to Angular Velocities observed m
Rocking Mirror
34. Relation between Height and Zenithal Angular Velocity
35. Example of Final Data produced by Opik from the Rocking-nurror
Observations
36. Distribution of Heliocentric Space Velocities \ of 279 Naked-eye
Observations
37. Distribution of Projected Heliocentric Velocities V 0 of 279 Naked-eye
Observations
38. Distribution of Heliocentric Space Velocities V„ for 680 Telescopic
Observations
39. Distribution of Projected Heliocentric Velocities V„ for 580 Telescopio
Observations
40. Percentage of Heliocentric Velocities exceeding 62 km./sec. according
to the preliminary rocking-mirror results
41. Relation between u> f and h for 486 Observations in the complete
Arizona Data
161
152
163
165
156
156
157
168
160
161
161
162
163
164
42. Provisional Distribution of Heliocentric Space Velocities for the
1,436 Arizona Velocities (all directions)
43. The Distribution of Geocentric Tangential Velocities v and tho
Correction for Error Dispersion
44. Stream Intensity nJC (for 77 = 0 ° to 77 = 77) for ft = 1 , B = 1 at
z = 45° N.
45. Stream Intensity nJC (for 77 = 0° to 77 = 77 ) for ft = 2, B = 1 at
z = 45° N.
46. Calculated Stream Intensity
47. Relative Frequency of Projection Ratios (sin 77 )
48. Distribution of Space Velocities
49. Distribution of Heliocentric Velocities
60. Distribution of Heliocentric Velocities for all Directions
61. Frequency of Solar and Hyperbolic Meteors in the Arizona Data
165
168
169
170
172
174
175
176
178
180
62. Relation between Uncorrected Geocentric Velocity v and Zenithal
Magnitude m,
53. Distribution of Heliocentric Velocities for High and Low Luminosity 181
XI
LIST OF TABLES
. Observed Frequency of Transverse Hel.ocentnc Components of
Velocity for Opik’s Arizona and Tartu Observati
. Distribution of Space Velocities for 583 Sporadic Meteors observed
by Opik in Arizona and Tartu , __ . a
Relation between the Heliocentric Tangential Velocity V 0 and
Zenithal Magnitude m, for Opik's Combmed Results
, Mean Errors and Standard Deviations for the Multiple Accordances
Average and Median Errors for the Multiple Accordances
Comparison of r.m.s. Errors for Duplicate and Multiple Accordances
Relation between Height and Velocity for the Shower and Sporadic
Meteors
Relation between Shower and Sporadic Meteors over the same range
of c and m
Distribution of v/v p for Sporadic and Shower Meteors
Data on Seven Sporadic Meteors photographed by Millraon and
HofRoit botwcon 1932 and 1936
Example of Whipple’s Trail Coordinates and Residuals for Meteor
No. 642
Velocities and Deceleration of Moteor No. 642
Whipplo’s Double Station Data for Seven Sporadic Meteors
Additional List of Sixteen Sporadic Meteors extracted from Jacchia’s
First Analysis
Additional List of Ten Velocities extracted from Jacchia’s Second
Analysis
Anticipated Performance of Super Schmidt Camera compared with
existing Cameras
Adopted Values of Errors in the Velocity Measurements
Collecting Areas of Aerial System
Distribution of Electron Densities observed in the Experiments on tho
Velocity Distribution
Comparison of Magnitudes obtained from Visual Rates and Electron
Densities
Number of Meteors observed in Different Magnitude Groups during
the Radio-echo Apex Experiments
Details of Seven Velocities in oxcess of 80 km./sec.
Mean Errors of Velocity Measurement at 70 km./sec.
Typical Transformations for McKinley’s Velocity Distribution
78. The Major Meteor Streams
79. Maximum Rates of the Quadrantid Shower determined by the Radio¬
echo Apparatus
80. Radiant Coordinates for the Quadrantid Shower determined by the
Radio-echo Technique
81. Parabolic Elements for the Quadrantids as computed by Wenz,
Davidson, and Hoffmeister, compared with Comet 1860 I
183
186
188
191
192
192
194
195
196
201
204
204
206
208
209
211
220
227
231
233
233
235
236
243
249
252
254
256
XU
82.
83.
84.
85.
86 .
87.
88 .
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100 .
101 .
102 .
103.
104.
105.
106.
107.
108.
109.
110 .
111 .
112 .
113.
114.
LIST OF TABLES
Orbital Elements for the Quadrantide computed from the Radio echo
and Photographic Data
Maximum Hourly Rates of the Lyrid Meteor Shower
The Lyrid Shower of 1922
Lyrid Radiants
Radio-echo Determinations of the Velocity of Lyrid Meteors
Orbital Elements for Comet 1861 I and the Lyrid Meteor Shower
Epoch of Maximum of the 77 -Aquarid Shower
Ephemeris of the ij-Aquarid Radiant
Orbital Elements of the Tj-Aquarid Shower compared with Halley’s Comet 267
272
273
275
279
280
283
257
260
260
261
263
263
265
266
Radiant Coordinates of the 8 -Aquarid Stream
Visual Velocity Measurements of possible 8 -Aquarid Meteors
Orbital Elements for the 8 -Aquarid Meteor Stream
Hourly Rate of the Perseid Stream since 1900
Radiant Positions of the Perseid Shower
Visual Velocity Measurements of Possiblo Perseid Meteors
Perseid Velocities Photographically determined by the Double-camera
Mothod
Radio-echo Measurements of Perseid Velocities
The Orbital Elements of the Perseid Stream and of Comet 1862 III
Radio-echo Observations of the Orionid Activity
Orionid Radiants 1928 according to McIntosh
Prentice’s Radiants for the Orionid Stream
Hoffmeister’s Radiants for the Orionid Stream
Visual Velocity Measurements of possible Orionid Meteors
Comparison of the Orbits of the ^-Aquarids, Orionids, and Halley’s
Comet
Denning’s 1928 List of the Radiants in Taurus and Aries
Whipple’s First List of seven Photographic Taurid Radiants
The Radiants in Taurus and Aries according to the Photographic
Analysis of Miss Wright and Whipple
Predicted Mean Radiant with Date for the Taurid-Arietid Streams
according to Miss Wright and Whipple
Velocities of the Taurids and Arietids according to Miss Wright and
Whipple
Orbital Elements for nine Taurid-Arietid Meteors computed by Miss
Wright and Whipple
Minimum Distances of Taurid Meteors from Planetary Orbits
Activity of the Geminid Meteor Shower as observed by the Radio-echo
Technique
Ephemeris of the Geminid Radiant compiled by King in 1926 and by
Maltzev in 1931 from Visual Observations
284
285
287
290
291
291
293
294
295
298
299
300
300
302
304
307
310
311
LIST OF TABLES
116. Whipple's Photographic Determinations of the Geminid Radiant from
Five Doubly Photographed Trails
116. Whipple’s Determination of the Daily Motion of the Geminid Rad.ant
from Thirty-six Single and Five Doubly Photographed Trai
117. Radio-echo Observations of the Gominid Radiant Position
118. Daily Motion of the Geminid Radiant
110. Photographic Determinations of the Velocities of Geminid Meteors
120. Orbital Elements for the Geminid Meteors
121. Hourly Rates of the Be&vM Meteor Stream. 1946 Decembor 22
122. Hourly Rate of the Ursid Stream subsequent to 1945
123. Radiant Positions of the Ursid Meteor Stream
124. Orbital Elements for the Ursid Meteor Stream and for Comet Tuttle
1939 k
125. Activity of the Giacobinid Shower
126. Visual Determinations of the Giacobinid Radiant during the 1933
Return
127. Photographic Determination of the Giacobinid Radiant during the 1940
Return
128. Computed Velocities of the Giacobinid Meteors 1946
129. Radio-echo Measurements of the Giacobinid Velocities 1946
130. Changes in the Orbit of Comet Giacobini-Zinner since 1900
131. Elemonts of the Giacobini-Zinner Comet 1946 and Predicted Elements
for 1953
132. Activity of the Leonid Shower
133. Visual Observations of the Leonid Radiant according to King
134. Change of Mean Radiant Position of Leonids with Date according to King
135. King*8 predicted Ephemoris of the Leonid Radiant
136. The Visual Leonid Radiant 1934 according to Huruhata
137. Corrected Leonid Radiant at Maximum from the Harvard Photographic
Data
138. Predicted Mean Radiant Position (1950 0) from the Harvard Photo¬
graphic Data
139. The Velocities of Six Leonid Meteors determined by the Double-station
Technique
140. The Orbits of the Leonids and of Temple's Comet 18661
141. The Activity of the Bielid Stream
142. Radiant Position of the Bielid Stream
143. The Changes in the Orbit of Biela’s Comet
144. Orbital Elemonts of Biola’s Comet and the Associated Meteor Streams
145. Radiant Positions of the Pons-Winnecke Shower 1916
146. Ephemeris of the Pons-Winnecke Radiant
147. Changes in the Orbital Elements of the Pons-Winnecke Comet
311
312
312
312
315
317
320
320
322
324
332
332
333
335
335
336
336
339
341
342
342
342
343
344
346
347
350
352
363
354
356
356
357
XIV
LIST OF TABLES
148. Activity of the Day-time Meteor Radiants
149. Mean Radiant Positions of the Day-time Meteor Streams
160. Daily Radiant Positions of the Day-time Streams 1960-2
161. Ephemerides of the Motion of the Radiants of the Day-time Arietids,
£-Pereeids, and /J-Taurids
162. The Velocity Measurements of the Summer Day-time Streams
163. Observational Data and Orbital Elements for the o-Cetid Shower
164. Observational Data and Orbital Elements for the Arietid Stream
166. Observational Data and Orbital Elements for the £-Perseid Stream
166. Observational Data and Orbital Elements for the Day-time 0-Taurid
Stream and the Night-time Taurids
167. Distribution of Luminosities in the Pereeid Shower according to Opik
168. The Frequency Distribution Observed by de Roy and by Sandig and
Richter during the 1933 Giacobinid Shower, os corrected by Watson
169. Distribution of Apparent Photographic Magnitudes for the 1940
Giacobinid Shower
160. Distribution of Integrated Absolute Photographic Magnitudes for the
1946 Giacobinid Shower
366
370
371
373
377
379
379
381
381
386
386
387
388
161. Scaling Factors for the Major Showers over the Sporadic Background
derived from Fig. 184 392
162. Meteoric Mass entering the Earth’s Atmosphere in Various Magnitude
Groups due to the Major Showers 393
163. The Density and Total Mass in the Orbits of the Major Showers 395
164. Data for Calculation of Time of Fall of a Particle into the Sun as a Result
of the Poynting-Robertson Effect 406
166. Times of Fall into the Sun of Meteoric Particles in the Major Shower
Orbits 408
166. Times of Separation of Meteors of Magnitude —2 and +6 due to
Poynting-Robertson Effect
167. Cometary-Meteor Stream Associations
409
413
168. Comets with Elliptical Orbits approaching the Earth to within
0100 a.u.
169. Observed Perturbations for Encke’s Comet
170. Elements of Comet Encke and three Taurid Meteors referred to
Jupiter’s Orbit (1920) and the Values of the Perturbation Constants
171. Major Meteor Showers without Cometary Association
172. Perturbations of the Geminid Orbit by Jupiter and the Earth in
100 years and changes in the least distance of the Orbit from the
Earth
173. Relation of Comet Brightness and Meteor Characteristics
174. Comparison of the Orbits of Short-period Sporadic Meteors, Asteroids,
and Comets
176. Times of Fall into the Sun for Meteors with an Asteroidal Type of
Origin
419
422
423
428
430
431
LIST OF PLATES
Between pp. 72 and 73
i. Meteor echoes photographed on an intensity-modulated
range-time display
n. The aerial system of the radiant survey apparatus at
Jodrell Bank
in. Diffraction pattern from a meteor trail obtained with
pulsed radio-echo equipment
I
INTRODUCTION
Olivier’s classical text on meteors appeared in 1925. f In the succeeding
quarter of a century the subject of meteor astronomy was dominated by
the great Arizona expedition for the study of meteors, and particularly
by the work of Opik.J Since the publication of Olivier’s book, the
literature of the subject has been composed largely of the results of the
Arizona expedition and of two books by Hoffmeister§ dealing mainly
with his own observations. In the years immediately preceding the
Second World War, the observations of the amateur observing teams
—particularly of those in America under Olivier, and in Great Britain
under Prentice||—together with the first results of Whipple’s new photo¬
graphic techniques at Harvard, cast serious doubt on the interpretation
of the Arizona results and also of those of HofFmeistcr. A controversy
arose as to whether sporadic meteors were interstellar or solar in
origin, and interest in the subject was further increased when the new
techniques of radio astronomy were applied to the observation of meteors
after the war. For some time the interest of the workers using this new
technique was dominated by the ability to observe meteors systematically
under all sky conditions, and particularly by the discovery of the great
series of meteor streams active in the day-time sky. The evolution of
the radio techniques for measuring meteor velocities and radiants soon
enabled the radio astronomical work to be concentrated on the classical
problem of the spatial orbits of the shower and sporadic meteors. Mean¬
while the precision work at Harvard on meteor photography was ex¬
tended and led to a deeper insight into the movement of meteors in
the solar system.
Now a great many outstanding problems have been solved, and it
seems unlikely that the next decade will witness such a revolution in
meteor astronomy as has occurred during the past six years. Although
the fundamental problem of the cosmical origin of meteors is not yet
solved, much of the basic information on which the solution must be
attempted already exists. The time would therefore seem to be appro¬
priate for a new text describing the new methods and the integration
of their results with the old problems.
t Olivier, C. P., Meteors, Williams and Wilkins, 1925. t See Chap. IX.
§ Hoffmoister, C., Die Meteore, Leipzig, 1937; Meteorstrdme, Weimar, Leipzig, 1948.
|| Valuable work in this period was also carried out by teams in Czechoslovakia under
Guth, in Japan under Yumanoto, and in Russia under Astapovich and Sytinskaya.
3505.00 B
2
INTRODUCTION
I
The question of the velocity distribution of sporadic meteors is of
such cardinal importance that considerable space has been devoted to
the topic. The work of Opik on this subject has been dealt with in
particular detail. This seemed the only just course since the contem¬
porary conclusions are in contradiction to his results; also his original
papers are not readily available.
It must be emphasized that this book deals specifically with the
astronomy of meteors. The subject of meteor physics will, it is hoped,
be the topic of a complementary text at some future date. Thus the
subject of meteor heights is introduced here only in so far as it is con¬
cerned with the determination of meteor velocities. An account of the
extensive work in which the heights of appearance and disappearance
of meteors are involved, in upper atmosphere measurements, and in the
theories of meteor evaporation is reserved for this other work.
It must also be emphasized that the book does not deal with meteorites.
Contemporary opinion is that these bodies, which are large enough to
penetrate the atmosphere without complete evaporation, are likely to
have a different origin from the meteors, or shooting stars, visible in
the sky. In any case very little is known about the astronomy of meteor¬
ites, the subject at present being largely of geochemical interest.
At the other end of the scale the micro-meteorites wliich are small
enough to be stopped before evaporation begins, and which are believed
to fall to earth as fine dust, are of recent discovery. Insufficient is
known about these micro-meteorites to justify the inclusion of the
subject in this book, particularly as almost our entire knowledge of them
is contained in two papers by Whipple.|
t Whipple, F. L., Proc. Nat. Acad. Sex. Wash. 36 (1950), 687; 37 (1951), 19.
II
OBSERVATIONAL METHODS I
VISUAL AND PHOTOGRAPHIC TECHNIQUES
1. Direct visual techniques
(a) Introduction
From the historical records which are referred to in later chapters of
this book it will be clear that meteors have been observed by the unaided
eye for many hundreds of years. It was the end of the eighteenth century,
however, before Brandes and Bcnzenberg in Germany noticed that,
although separated by considerable distances, they saw the same meteor
but that it appeared in different parts of the sky. From these and similar
observations they deduced that the meteors were appearing at altitudes
of 80 to 100 kilometres and that they must be due to bodies from space,
entering the earth’s atmosphere at speedsof many kilometres per second.
In November 1833 the great shower of Leonid meteors occurred. On this
occasion it became evident to Olmsted, Twining, and many others that
the meteors were apparently radiating from a point. In the second half of
the nineteenth century the work of Schiaparelli, Newton, and others
drew attention to the importance of determining the spatial orbits in
which the meteors were moving before they entered the atmosphere.
It became evident that, apart from the counting of meteors, the accurate
determination of their radiants and velocities was a prerequisite of any
serious progress in meteor astronomy. From this era the techniques
of naked-eye observation have been steadily improved and the con¬
temporary work of experienced observers is a remarkable example of
the excellence of the results which may be obtained in the recording
of the transient and infrequent meteoric phenomena.
A single observer can only record the apparent path of a meteor pro¬
jected against the star background. On the other hand, duplicate observa¬
tions enable the parallactic displacement of the two apparent paths to
be determined and, in principle, gives data on the radiant, height, path
length, and velocity of the meteor. Originally, the method of recording
appears to have been the plotting of the observed path of the meteor on
a star map. As early as 1890, Denningf recommended the use of a
f Denning, W. F., Telescopic work for Starlight Evenings, London, 1891. Mem. Brit.
Aslr. Ass. 1 (1891), 20.
4 OBSERVATIONAL METHODS—I II, § 1
wand, or extended string, which the observer aligned along the meteor
path and read the coordinates of the beginning and end of the path in
terms of the star background. This gave more time for the establish¬
ment of the position of the trail, and also gave a more accurate ‘flight
direction’ by enabling the meteor path to be extended to more suitable
star fields. This method has been steadily improved, particularly
under the influence of Prentice in Great Britain, such as by the use of
cross bearings and the quotation of actual distances between known
stars instead of estimates of angular distance. Thus the modern British
observer rarely uses maps at the time of observation but presents his
data in terms of the coordinates of stars for subsequent reduction to
true paths. On the other hand the American observers, under Olivier,
plot the path of the meteor on a prepared chart. An investigation of the
accuracy of the data obtained by two of the best British observers
between 1932 and 1935 has been carried out by Porter.f From an analysis
of 102 meteor paths simultaneously observed by Prentice and Alcock,
Porter plotted the frequency distribution of errors for the position of
the beginning and end of the meteor path. The probable error for the
beginning was ±3-26° and for the end ±2-43°. These are comparable
with the errors which Porter found in his subsequent analysis of the
entire British meteor data,J referred to in Chapter X. In a later analysis
of the accuracy of radiant determinations Porter§ concluded that the
probable error was ±2-4° and that the mean deviations in the height
determinations were 3-6 km. at the beginning of the path and 2*8 km.
at the end. As regards the accuracy of the radiant, Porter’s conclusions
were criticized by Prentice|| on the grounds that Porter had assumed
the Perseid radiant to be a point whereas, in fact, it is diffuse. Actually
it seems that the probable error in the radiants determined by good
observers is about ±1°.
The accuracy of observations by inexperienced meteor observers has
been discussed by Watson and Cook, ft As a result of tests made during
the Leonid shower in 1933 they found probable errors in the direction
given for the meteor path of between ±10-8° and ±18-8°.
Unfortunately the timing errors are necessarily large in the visual
techniques even with the best observers, mean errors of 20 to 30 per
cent, being quoted by Porter. It will be evident from succeeding chapters
f Porter, J. G., J. Brit. Aatr. Asa. 48 (1938), 337.
X Porter, J. G., Mon. Not. Roy. Aatr. Soc. 103 (1943), 134.
§ Porter, J. G., J. Brit. Aatr. Aaa. 49 (1939), 113.
|| Prentice, J. P. M., ibid. (1939), 146.
tt Wataon, F., and Cook, E. M., Pop. Aatron. 44 (1936), no. 6.
H §1 VISUAL AND PHOTOGRAPHIC TECHNIQUES 5
of this book that little confidence can be placed in many of the visual
velocity determinations.
(6) The Reduction of Visual Observations
The difficulties in the reduction of the observed paths to true paths
in the atmosphere will be clear from Fig. 1. Observers at 0„ 0 2 , record
the beginning and end of the meteor path at M' lt Mi and M[, MJ, respec¬
tively. If the observations are simultaneous 0, MJ and 0 2 Mi will meet
to define the beginning of the meteor path and OjMJ and 0 2 MJ will
meet to define the end. In this case the computation presents no difficulty.
These ideal conditions are rarely fulfilled since one or other of the
observers generally misses a portion of the flight. Various methods
have been employed in the reduction! and arbitrary adjustments to the
observations by the computers appear to have been common practice
until about 1930. The method recommended by PorterJ and the one
now generally used in the reduction of the British observations is that
devised by Davidson.§ The detailed procedure in the practical applica¬
tion of the method has been described by Portcr.|| In principle this
method finds the point of intersection of the observations of Oj with
the plane of the observations of 0 2 , and no assumptions of simultaneity
are made.
Using this method Porter ft bas reduced the entire duplicate and
multiple observations of meteors made in Great Britain between 1890
f For oxample, Schaeberlo’s method as described by Olivier, C. P., Meteors, ch. 14.
$ Porter, J. G., Mon. Not. Roy. Astr. Soc. 103 (1943), 134.
§ Davidson, M., J. Brit. Astr. Ass. 46 (1936), 292.
|| Porter, J. G., Mem. Brit. Astr. Assoc. 34 (1942), 37.
ft Porter, J. G., 3/on. Not. Roy. Astr. Soc. 103 (1943), 134; 104 (1944), 257.
6
OBSERVATIONAL METHODS—I
II, § 1
and 1940. The results and the analysis of the errors are discussed in
Chapter X.
(c) The Magnitude Correction
The stellar magnitudes quoted by observers differ considerably on
account of varying distance, atmospheric absorption, etc. It is custo¬
mary to reduce the observed magnitude to zenithal magnitude, that is
the magnitude the meteor would have if it were in the observer’s zenith
but at the same height. The reduction, which is simply made by applying
the inverse square law, has been discussed by Opik.t Porter, J and others.
If the meteor is seen at a distance R and height h, the effect of bringing
it to the observer’s zenith would be to increase the luminosity in the
ratio R 2 /h 2 . Then the stellar magnitude would be diminished by an
amount Am* where, (2-512) Am » = R 2 /h 2 .
Thus Am, = 5 log R/h = 5 log sec z
where z is the zenith distance of the observation.
The correction factors given by Porter, J which also include a small
effect due to atmospheric absorption, are given in Table 1.
Table 1
Correction to Zenithal Magnitude
Height h km.
60
mm
100
120
140
160
180
200
Distance R km.
60
+ M
• •
• •
• •
o •
80
+ 0-4
+ 0-5
• •
• •
• •
• •
• •
• •
100
-01
-01
0
• •
• •
• •
• •
• •
120
- 0-6
- 0-6
-0-4
-0-4
• #
• •
• •
• •
140
-10
eij
- 0-8
-0-7
-0-7
• •
• •
• •
160
-1-4
- 1-2
— M
-M
-10
- 1-0
• •
9 .
180
-1*7
- 1-6
- 1-6
-1*4
-1-4
-1-3
-1-3
• •
200
-20
- 1-8
-1*7
- 1-6
- 1-6
- 1-6
-15
-1-5
220
-2-3
-21
-1-9
-18
- 1-8
-1*7
-1-7
240
-2-5
-2-3
— 2-2
-21
- 2-1
-20
-20
-1-9
260
- 2-8
- 2-6
-2-4
-2-3
-2-3
- 2-2
- 2-2
-21
280
-30
- 2-8
- 2-6
- 2-6
-2-4
-2-4
-2-3
-2-3
300
-3-2
-30
- 2-8
-2-7
- 2-6
- 2-6
- 2-6
- 2-6
320
-3-4
-3*2
EH
-2-9
- 2-8
-2-7
-2-7
- 2-6
340
-3-7
-3-4
-3-2
-31
-3-0
-2-9
-2-9
- 2-8
360
• •
-3-4
-3-2
-3-1
-3-0
380
• •
-3-5
-3-3
-31
400
• •
-3-9
-3-6
-3-5
-3-4
-3-3
-3-2
t Opik, E. J., Publ. Tartu Obs. 25 (1922), no. 1; ibid. (1923), no. 4.
X Portor, J. G., Mem. Brit. Astr. Ass. 34 (1942), 62; J. Brit. Astr. Ass. 48 (1938), 337.
7
II, §1
_ $ , VISUAL AND PHOTOGRAPHIC TECHNIQUES
The variation in the m agnit ud e e S tima^of £g,ven meteor^ y
different observers has been discusse y P* t during
the discrepancies in the observation of 3 , 8 U meteore o 2
the Arizona meteor expedition Opik deduces the retom*
between the observational error e as a function of the magmt
Table 2
Uf M. «—<i— . .«<
fn UDll:
m
<
>4-7
±0-36
4-2
±0-37
3-7
±0-47
3-2
±0-56
2-7
±0-63
2-2
±0-65
m
e
1*7
±068
1-2
±0-77
0*7
±0-87
0-2
±0-96
-0-3
±103
< -0-8
±105
Id) The Counting of Meteors
The relation between the actual numbers of meteors and th ° e 8CC "
by an observer has been investigated by several workers. Backhouse}
appears to have been one of the first to investigate an observer s field of
vision for meteors of different magnitude. He est.mated the effective
field for very bright meteors (magnitude -4-5) to be 100 . decreasing
to 25° for faint meteors of magnitude +5. His relationship is shown in
F The most thorough statistical investigation of the problem is by
0pik.§ If two observers watch the same area of sky the number oi
meteors seen in common will decrease as the brightness decreases.
Opik expresses this in terms of a Coefficient of Perception p. Then il
n„n 2 are the numbers seen by two observers, and n„ the number seen
in common nQ = Pl n 2 = p 2 n x
and the true probable number N will be given by
N = — = — = n * n2 -
Pi P 2 n o
Opik also shows that if there are k observers then the true number N
will be given by g
N = i_(i_Pi)( 1 _p J )...(i-p k )’
where S is the number of different meteors recorded by all the observers.
t Opik, E. J., Ann. Harv. Coll. Obs. 105 (1936), 549.
x Backhouse, T. W., Observatory, 7 (1884), 299.
§ Opik, E. J., Publ. Tartu Obs. 25 (1922), no. 1; (1923), no. 4.
8
OBSERVATIONAL METHODS—I
II. §1
After experience of this so-called ‘double-count’ method during the
Perseid shower of 1920 Opik concluded that the Coefficient of Perception
could be represented as
p = T7r,
where the magnitude function T depends only on the apparent magnitude
and is the same for all observers, while the coefficient of attention ir is
an individual function depending on the observer and his position.
Fio. 2. Relation between limiting brightness of a moteor visible
at a given anglo from an observer’s line of vision according to
Hoffmeister (-), Opik (-), and Backhouso
In plotting Hoffmeistcr’s data it has been assumed that a moteor of
zero magnitude con just be seen at 60° from tho lino of vision.
The treatment of the observations of the Perseid showers in 1920 and
in 1921 is very lengthy. It involves the evaluation of T and tt from a
comparison of the observations of a number of observers on different
nights with varying sky conditions. Here it is sufficient to summarize
the conclusions about the effective field of vision as a function of magni¬
tude. This result is given in Fig. 2 for comparison with the estimates of
Backhouse.
The subject has also been treated in detail by Hoffmeisterf in con¬
nexion with his extensive observations of the diurnal variation in
meteor rates which are discussed in Chapter VI. He considered the
f Hoffmeister, C., MeleoratrOmc, and private communication.
n § , VISUAL AND PHOTOGRAPHIC TECHNIQUES 9
effects of fatigue, t increase in brightness with velocity of meteors and
decrease of apparent brightness with mcrcasmg angular velocity. In
connexion with this work Hoffmeister carried out experiments with
■artificial meteors'. The various correction factors derived by him are
given in Chapter VI, and the relation between the limiting brightness
of a meteor visible at a given angle from the line of vision is plotted in
Fig. 2 for comparison with the data of Backhouse and Opik.
The subject has also been considered by Ceplecha.t whose results are
in close agreement with those given in Fig. 2.
From a consideration of the results of Backhouse, Opik, and Hoff¬
meister, Almond, Davies, and Lovell§ have estimated tho actual
collecting area of an observer for various meteor magnitudes. From
the curves in Fig. 2 the limiting meteor magnitude visible at a given
anglo from an observer’s line of vision was obtained as in Table 3.
Table 3
Limiting Meteor Magnitude Visible at a given Angle from an
Observer's Line of Vision
Anglo from line of vision . 60°
58°
53®
44®
30°
11®
0®
Limiting magnitude. . 0
1
2
3
4
5
6-5
If the observer’s line of sight is directed upwards at 45°, the inter¬
sections of these cones of limiting visibility on a surface 95 km. above
the earth can be plotted. The apparent magnitudes are then corrected
to zenithal magnitudes according to § 1 (c) above, and the actual
areas over which an observer sees meteors of a given magnitude can then
be measured graphically. The results are given in column 2 of Table 4.
Column 3 gives the relative number of meteors in the various magnitude
groups falling on a square kilometre of the sky. This column is estimated
on the basis of the data given in Chapter VII for the number and mass
distribution of sporadic meteors. If it is assumed that one meteor of
magnitude — 1 falls per sq. km. per hour, the number of meteors seen
in each magnitude group per hour can then be calculated as in column 4.
The summation of this column then gives the total rate which would be
seen by the observer on this assumption. If the actual observed hourly
f It is interesting to note that tho effects of fatigue appear to be very small in meteor
counts. Seo, for example, the tests made by Prentice, J. P. M., J. Brit. Astr. Ass. 52
(1942), 98.
J Ceplecha, Z., Bull. Cent. Astr. Inst. Czech. 2 (1950), no. 10, 145.
§ Almond, M., Davies, J. G., and Lovell, A. C. B., Mon. Not. Boy. Astr. Soc. 112
(1952), 21.
10
II, § 1
OBSERVATIONAL METHODS—I
rat© is known then the relative numbers in column 3 can be scaled down
to give the actual numbers in the different magnitude groups falling on a
sq. km. per hour. In column 5 this has been done for a case where the
observed hourly rate by a single observer is one.
Table 4
Numbers of Meteors of Different Magnitudes seen by a Visual
Observer
1
Zenithal
magnitude
2
Collecting area
(sq. km.)
3
Relative
number per
sq. km.
4
Relative
number seen
5
True number per
sq. km. per hour J or
hourly rate of one
MH
161
158
25.000
( x io-«)
31-8
6,160
100
616,000
20*2
wm
9,845
63-1
620,000
12-7
16,126
39-8
641,000
802
24,200
25-1
607,600
606
36.150
15-8
671,000
318
60,000
100
600,000
202
i
66.000
6-31
420,000
1*27
i
87,600
3-98
348,000
0-80
0
115,700
2-51
291,000
0-60
-j
135.800
1-58
214,000
032
-l
200,000
100
200,000
0-20
4,953,600
2. The special visual techniques of the Arizona expedition
The famous Harvard expedition to Arizonaf for the study of meteors
took place between 1931 and 1933. For this expedition Opik evolved
special techniques of observation. It will be evident from later chapters
of this book that many of the results of this work are in dispute. For this
reason, and because the techniques have not been used since (except
by Opik in Tartu), they are treated separately here from the more
conventional British and American methods.
(a) Observation of Meteor Paths
For the determination of meteor paths and heights, visual observers
were placed at two stations over a 40 km. east-west base line. The
meteors were registered in two areas of about 60° effective diameter
centred on the meridian at 45° zenith distance north and south. Iron
reticules projected on the sky were used as coordinates of reference for
tracing the meteor trails. In this respect the technique differs markedly
f Shapley, H., Opik, E. J., Boothroyd, S. L., Proc. Nat. Acad. Set. Wash. 18 (1832), 16.
11
„ § 2 VISUAL AND PHOTOGRAPHIC TECHNIQUES
fr ' m the visual methods described in § 1. The reticules represented
Llination and hour angle at 10* intervals. The hour angle was trans¬
ferred to right ascension from the recorded time of observation. Thes
reticules were mounted on two opposite slopes of a wooden shelter whi
provided protection for the observers within. The observer looked
through one eye-hole of 32 mm. diameter placed at a distance of 50 cm.
from the centre of the reticule. In surveying the area it was only necessary
for the observer to move his eye. the parallax introduced being only a
fraction of a degree. It was considered that the reticules permitted
direct reading of celestial coordinates to within half a degree, or with
systematic corrections to within one tenth of a degree.
The widths of the wires forming the reticule were 0-5° to 0-8 and could
be easily seen on the sky without artificial illumination. The obscuration
was 10 per cent. Prepared maps gave exact reproductions of the reticules
on a 1 :4 scale, and the observer traced the trails on these maps. The time
of appearance to the nearest second, magnitude and duration were also
recorded. The total area of sky covered by each reticule was 80° X 80 ,
of which the observer could watch a field of about 60° diameter.
In the Arizona programme the observations were extended to infra
visual meteors by using two 4-in. telescopes situated at an east^wcst
spacing of about 3 km. The field of view was 4° using an eye-picce with
a magnification of 17 times. Reticules in the focal plane were used as
reference coordinates.
A comprehensive analysis of the errors involved in using these reticules
has been given by Opik.f An indication of the accuracy claimed is
given in Table 5, which refers to the errors in the displacement of the
beginning and end points for meteors observed in common by more than
one observer.
Table 5
Displacement of the Beginning and End Points for Common Meteors
wth Unequal Recorded Lengths in the Reticule Observations
(The mean values are given in tho sense: longer trail minus shorter trail without regard
to observer.)
Difference in length limits
0-6°-2-2°
2-3°-4-8°
> 4-9°
Difference in length, mean
118°
3-34°
7-56°
Mean displacement of beginning
-0-39°
—1-96°
-4-42°
Mean displacement of end
+ 0-79°
+ 1-38°
+ 314°
Mean displacement of centre .
+ 0-20°
-0-29°
— 0-64°
Numbor of meteors
720
564
394
t Opik, E. J., Ann. Harr. CoU. Obs. 105 (1936), 549.
OBSERVATIONAL METHODS—I
II, §2
These are comparable with the errors quoted by Porter for the
beginning and end points of the meteor paths in the British data referred
to in § 1 (a). On the other hand Opikt gives a probable error of 8°
in the radiant determination by the reticule observations compared
with the 1° claimed by the British observers.
The use of reticules for meteor observation has been criticized by
Olivierf on the grounds that they force the employment of only one eye
at a time by the observer. He justifies his criticism by reference to his
own experience and also by referring to Opik’s coordinatesf for the
radiants of some of the major showers which differ considerably from
the accepted radiant positions. Criticisms have also been made by
Prentice,§ particularly that the base line, of less than 40 km., was too
short.
(6) Observation of Meteor Velocities
For the measurement of angular velocities Opik devised an ingenious
technique which is now commonly known as the rocking-mirror method.
The apparatus, which is described in detail by Shapley, Opik, and Booth-
royd,|| consisted of a 6-in. square plate-glass mirror, resting freely on
three supports forming an isosceles right triangle. The support at the
right angle was motionless while the two others were tilted in the
vertical direction to make harmonic oscillations with a difference of
phase of 90°. Thus the normal to the mirror plane was given a conical
motion of small amplitude. Assuming that the two oscillations are of
equal amplitude, then a reflected stellar image will describe a circle if
the object is in the zenith, and an ellipse if it is outside the zenith. A meteor
will describe a more complicated curve, produced by the superposition
of the elliptical oscillation upon its own motion. The shape of the
apparent trajectory depends on a number of factors including the
angular velocity of the meteor and its direction. The trajectories are
pseudocycloidal of the type shown in Fig. 3, forming closed loops if the
meteor is moving slowly and open loops for fast-moving meteors. Since
the period of oscillation of the mirror is known, the angular speed can be
derived from the trajectory shape, or from the length, of a complete
oscillation. The calculation of the velocities is discussed in detail in
Chapter IX.
In the Arizona apparatus the period of oscillation was 0*1 sec. and the
t Opik, E. J., Circ. Harvard CoU. Oba. (1934), no. 388.
X Olivier, C. P., Pop. Aatrorx. 46 (1938), 325.
§ Prentice, J. P. M., Rep. Phya. Soc. Progr. Phya. 11 (1948), 389.
|| Shapley, H., Opik, E. J., and Boothroyd, S. L., loc. cit.
XI §2 VISUAL AND PHOTOGRAPHIC TECHNIQUES
oscillations were transmitted to the two supports from the same end of
an eccentric shaft, the phase difference being attamed by placing the
two levers at right angles. The shaft was driven by a 60-r.p.s. synchronous
motor through a gear reduction of 1:6, and the major axis of the mirror
oscillation was 0-5°.
Fio. 3. The appearanco of (a) a slow meteor, (6) a fast meteor
in Opik’s rocking mirror apparatus.
The ellipses of oscillation for stars could be seen down to fourth
magnitude out to an angle of 5° from the line of direct vision. The
circumstances for meteor observation are stated to be more favourable
because the linear dimensions of the oscillation are increased along the
trail and the resolving power of the eye is therefore greater. Experience
showed that about 80 per cent, of the meteors seen by a reticule observer
could be observed in the rocking mirror with sufficient certainty to be
traced on a map. Complete velocity data could be obtained for about
half of these. It is claimed that fifth-magnitude meteors over an effec¬
tive area of diameter 30° could be observed with the apparatus.
Opik’s extensive treatment of the errors and results obtained with this
rocking-mirror apparatus at Arizona and later in Tartu are described in
Chapter IX.
In the Arizona expedition these visual observations were extended
to infra visual meteors by adapting the rocking mirror so that it could
be used in conjunction with a 4-in. telescope. In this modification a
bar, rigidly connected at right angles to the mirror surface, was given
a conical movement so that an elliptical oscillation of the image was
14
OBSERVATIONAL METHODS—I
II, §2
obtained. The observer then traced the apparent trajectory on a map
which was a copy of the focal reticule in the telescope. The results
obtained by Boothroyd using this device are also discussed in Chapter IX.
3. Photographic techniques
(а) Introduction
Although the main advances in photographic meteor studies have
come from the application of special double-camera techniques as
described later in this section, a great deal of valuable information has also
accumulated from the chance occurrence of meteor trails on photographic
plates exposed for other purposes. This is particularly the case with the
Harvard collection. Later chapters (especially Chaps. XIII to XVII)
contain many references to the analysis of these meteor trails in the
Harvard collection back to 1896. In referring to these trails the Harvard
notation is retained and the characteristics of the various cameras are
listed in Table 6 for reference.
Watsonf has given an account of meteors photographed with the
18-in. Schmidt camera on Mount Palomar, obtained by chance while the
camera was in use on the supernova patrol. The field of this camera is
about 9°. On 394 films, representing a total exposure time of 10,663
minutes, he found 81 meteor trails. From a comparison of this rate with
the known visual rates Watson estimated that the camera recorded
meteors down to second and third magnitudes.
(б) Special Photographic Meteor Techniques
Simultaneous photography of a meteor trail from two stations enables
the trajectory of the meteor to be determined. If rotating shutters are
used to cover the lenses at short intervals of time, a direct measure of the
angular velocity of the meteor at various points along the trail is also
obtained. Elkinf at Yale appears to have been the first to initiate
successfully a programme of meteor photography with two cameras.
Hia equipment, which was erected in 1894, consisted of a long polar axis
driven by clockwork, carrying a number of cameras with apertures of
6 to 8 in. A simpler arrangement carrying four cameras was placed
2 miles north of the former. Some of the results obtained by Elkin with
this equipment are discussed in Chapter XI. In 1900 Elkin§ described
the modification whereby a rotating shutter was introduced. Elkin
states that the idea of a rotating shutter was first suggested in 1860 by
t Watson, F., Pop. Asiron. 50 (1942), no. 3.
% Elkin, W. L., Aetrophys. J. 9 (1899), 20; 10 (1899), 25.
§ Ibid. 12 (1900), 4.
II, §3
VISUAL AND PHOTOGRAPHIC TECHNIQUES
15
Table 6
Characteristics of the Harvard Cameras not Specifically Employed for
Meteor Photography
Description
Aperture
(in.)
Focus
(in.)
Remarks
Source of
information
E
The old series in use before
Fisher and
1900. A list of the various
lonses used is given in the
Olmstedf
reference.
A
24
135
Bloemfontein. S.A., since
A
1926.8.
AC
1-5
13
Oak Ridgo since 1934.7.
AV
CA
Al
1-5
13
Oak Ridge sinco 1934.7.
1-5
6
Oak Ridge since 1932.7, later
equippod with rotating shut¬
ter for meteor work.
AM
1-6
13
Bloemfontein, S.A., since
1925.2.
AX
3
12
Bloomfontein, S.A., sinco
1927.8.
AY
3
12
Cambridge, Mass., to 1928.
R
8
44
Bloemfontein, S.A., since
1930.1.
Wright
BI
1-5
Short focus
Bloemfontein, S.A., sinco
. and
attachod to
1930.1.
WhipploJ
8 in. (B)
FA
1-5
6
Cambridge to 1948.7, later
oquipped with rotating shut¬
ter for meteor work.
I
8
60
Cambridge.
IR
8
50
Oak Ridge.
J
24-33
84
Oak Ridge.
MA
12
84
Oak Ridge sinco 1938.6.
MC
16
83
Oak Ridgo since 1932.5.
MF
10
49
Bloemfontein since 1927.8.
RB
3
21
Bloemfontein.
RH
3
21
Oak Ridgo since 1932.7.
RL
4
28
Oak Ridge.
J. H. Lane and that in 1885 Zenker in Berlin attempted to use the idea
to photograph meteors but without success. The Yale apparatus con¬
sisted of a bicycle wheel rotating in front of the cameras. The wheel
carried twelve opaque screens and the speed of rotation was 30 to 50
r.p.m. The first successful occulted trail was photographed on 1899
July 31, and the meteor was also recorded on the second camera, 2 miles
distant. Some of Elkin’s early measurements are referred to in Chapter
XI. Elkin continued this work until 1909 but published very few results.
t Fisher, W. J., and Olmsted, M., Bull. Harv. Coll. Obs. (1929), no. 870.
j Wright, F. W., and Whipple, F. L., Tech. Rep. Harv. Coll. Obs. (1950), no. 6.
16
OBSERVATIONAL METHODS—I
II. §3
The analysis of the work was, however, made much later by Olivier, f
Unfortunately the base line of approximately 3-5 km. between the two
camera sites was inadequate for precision results.
The rotating-shutter technique was subsequently used by a number
of workers, such as by Lindemann and Dobson,J Whitney,§ Fedynsky
and Stanjukovitsch,|| Waters,ft Ceplecha,Jt Thomson and Burland,§§
and others. Systematic results were not achieved by any of these workers
(apart from the work of Jacchia, Kopal, and Millman|||| using Thomson
and Burland’s apparatus during the 1946 Giacobinid shower which is
described in Chapter XVI). The main development of the technique
has taken place at Harvard, where results of the highest quality and
precision have been obtained.
(c) The Harvard Techniques for Meteor Photography
Meteor photography at Harvard using two cameras, one equipped
with a rotating shutter, was commenced by Fisher in 1932. The cameras
each used a Ross Xpres F/4 lens of 6 in. focal length covering a plate
8 x 10 in. One camera was equipped with a two-vane rotating shutter
driven by a synchronous motor to give thirty occultations of the lens
per second. With this equipment Fisher secured his first photograph
in August 1932. The equipment was then assigned to Millman,tft who
used it during the Leonid shower of 1932 and 1933, successfully photo¬
graphing three Leonids and one sporadic meteor. Subsequently Millman
dismantled the original rotating-shutter camera and in the summer of
1935 equipped the AI patrol camera with a shutter mechanism so that
the lens was covered 20 times per second, the obscuration lasting for
0 0053 sec. and the exposure for 0 0447 sec. Approximately 90 hours
of exposure time was required for one successful meteor photograph
with this equipment. The method of analysis and the results obtained
with this apparatus up to 1936 have been described by Millman and
Hoffleit.ttt and are included in Chapter XI.
In 1936 the Harvard programme was continued by Whipple,§§§ using
t Olivier, C. P., Astron. J. 46 (1937), 41.
j Lindomann, F. A., and Dobson, G. M. B., Mon. Not. Roy. Ast. Soc. 83 (1923), 163.
§ Whitney, W. T., Pop. Astron. 45 (1937), 162.
|| Fedynsky, V. V., and Stanjukovitsch, K. P., Astr. J. U.S.S.R. 12 (1935), 440.
tt Waters, H. H., J. Brit. Astr. Ass. 46 (1936), 153.
Ccplecha, Z., Bull. Cent. Astr. Inst. Czech. 2 (1951), 114.
§§ Thomson, M. M., and Burland, M. S., J. Roy. Astr. Soc. Can. 34 (1940), 479.
IIH Jacchia, L. G., Kopal, Z., and Millman. P. M., Astrophys. J. Ill (1950), 104.
ftt Millman, P. M., Bull. Harv. Coll. Obs. (1933), no. 891; Publ. Amer. Astr. Soc. 7
(1933), 181.
JJJ Millman, P. M., and Hoffleit, D., Ann. Harv. Coll. Obs. 105 (1937), 601.
§§§ Whipple, F. L., Proc. Amer. Phil. Soc. 79 (1938), 499.
II §3 VISUAL AND PHOTOGRAPHIC TECHNIQUES 17
the AI patrol camera with the rotating shutter as described above, at
Oak Ridge, together with a similar patrol camera (FA) situated at
Cambridge, Mass., at a distance of 37-9 km. From 1936 February 15
the observing programmes of the two cameras were synchronized and
seventeen pairs of meteor photographs were obtained in 27 months—
representing 2,000 hours of exposure time. Each camera used Ross
Xpres lenses of aperture 1-5 in. and focal lengths 5-95 in. (AI) and 5-99 in.
(FA). The field of tolerable definition was about 60 degrees in each case.
The two cameras were directed toward a point in space about 80 km.
above the earth’s surface, and were driven on polar axes. The exposures
for each plate were 2 hours for AI and 1 hour for FA, the difference being
necessary on account of the greater background fog on the FA camera,
which was situated in the middle of a city. In 1939 the FA camera was
also equipped with a rotating shutter, and according to Whipplcf thirty
doubly photographed meteor trails had been obtained by the end of
1942. Many of these results, and those obtained subsequently with
these cameras, are referred to in Chapters XI and XIII-XVII. Chapter
XI also gives an account of the method of measurement and reduction
of the results.
This work of Whipple’s yielded important results of high precision,
but the programme suffered from the comparative insensitivity of the
cameras. Only meteors brighter than magnitude zero or — 1 could bo
satisfactorily recorded, giving an average yield of only 1 meteor per
100 hours exposure. In 1946 an investigation was commenced in an
endeavour to overcome these difficulties. This resulted in the design by
J. G. Baker of the Super Schmidt cameras which are now in operation
in New Mexico and which are described separately below. In order to
establish the routine, and to overcome the preliminary obstacles of
observation at remote sites, the Harvard team set up the observing
stations at Soledad and Dona Ana in 1948, using the Ross Xpres cameras
described above, together with another pair constructed from aerial-
camera lenses (K 24) of 3-in. aperture and 7J-in. focal length. Another
pair used K 19 lenses of 5-in. aperture and 13-in. focal length. The shutter
speed was increased to 1,800 r.p.m. for the K 19 cameras.J Whipple
states that these aerial lenses were more effective for meteors than the
old Ross Xpres ones, but that the gain was not proportional to the
aperture. Some of the results from these New Mexico stations are
t Whipple, F. L., Sky and Telescope, 8 (1949), no. 4.
t The Harvard notation for the plates of the new camera lenses in Now Mexico is
KA, KB, KE.
3505.00
c
18
OBSERVATIONAL METHODS—I
II. §3
included in Chapter XI. The relative performance of the various cameras
is indicated on p. 20.
(d) The Harvard Super Schmidt Meteor Cameras
In order to improve the sensitivity of meteor cameras beyond the
magnitude limit of zero to — 1 and at the same time retain a wide field
of view, Baker proposed the use of a new optical system known as the
Fio. 4. The Super Schmidt camera.
Super Schmidt.
published,! from which the following details are taken. The principle
is illustrated in Fig. 4. Light from a distant point is refracted through
the outer spherical shell A, the hyperchromatic correcting plate B, and
the inner spherical shell C. It is then reflected at the mirror D, and passes
again through C to the photographic plate on the focal sphere E. The
concentric shells A and C greatly reduce the under-corrected spherical
aberration of the mirror without destroying the spherical symmetry,
and hence make possible the wide-angle properties of the system. The
correcting plate B is weak compared with that in the ordinary Schmidt
system. It is made of cemented elements of crown and flint glasses. The
system gives almost complete correction over the range 3,800 to 7,000 A.
In fact, the specification called for the on-axis image of a point source
f Whipple, F. L., Sky and Telescope, 8 (1949), no. 4; Tech. Rep. Harv. Coll. Obs. (1947),
no. 1; Sky and Telescope, 10 (1951), 219.
II, §3
VISUAL AND PHOTOGRAPHIC TECHNIQUES
at infinity in the range 3,500 to 8,000 A, to be concentrated 50 per cent,
within a circle of diameter 0-015 mm. and 90 per cent, within 0 040 mm.
The spherical lenses are 18 in. diameter and the mirror 23 in. diameter
The effective aperture is 12-25 in. and focal length 8 in. The optical focal
ratio is 0-65 and the effective field 55° without appreciable vignetting at
the edges. However, the interposition of a 7jj-in. diameter photographic
film reduces the effective clear aperture to 9-8 in. and the effective foca
ratio to 0-81 in. Unusual problems are introduced by the position and
shape of the film. The focal surface is spherical and the amount of
flattening has to be compromised with additional complication in the
optical system. The radius of curvature of the focal sphere in the Super
Schmidt is 8 in., and to maintain the image quality it is necessary that
the photographic emulsion should follow the focal sphere within 0 0005
in. The difficulties and technique of producing a large number of suitably
shaped emulsions have been described by Carroll, McCrosky, Wells, and
Whipple.f Standard flat acetate film coated with the appropriate
emulsion is moulded to the required shape. A rubber diaphragm, heated
by a radiant heater in a water-cooled tank, presses the flat film under
the action of compressed air into a convex spherical polished mould of
the required dimensions. Only 2 minutes is required for the complete
cycle of diaphragm heating, compression, cooling, and cutting out the
spherical surface from the 10x 10 in. rectangular film. In the camera
the film is supported by a vacuum on a spherical surface covered by a
delicate spider-web of grooves emanating from the centre, to allow the
transfer of air tangentially below the emulsion base.
The curved films are copied after exposure on to flat glass plates within
a few weeks of processing by a special copying camera designed by Baker, f
Since the optical system is a true concentric spherical projection, the
star images appear on the spherical film in their relative configuration on
the celestial sphere. The copying on to a flat plate renders the final
projection accurately gnomic. Since a great circle on the sky becomes
a straight line after gnomic projection, no new problems of measurement
or reduction are introduced by the use of the Super Schmidt.
The large aperture of the system also makes a conventional type of
rotating shutter external to the camera unsatisfactory. A shutter in the
front of the camera would become a large and unwieldy ‘windmill’.
This difficulty has been solved by placing a small shutter immediately
in front of the photographic plate. The shaft passes through both the
t See Carroll, P., McCrosky, R. E., Wells. R. C., and Whipple, F. L., Tech. Rep.
Harv. Coll. Obs. (1951), no. 8.
20
II. §3
OBSERVATIONAL METHODS—I
mirror and the inner shell along the optical axis. The shutter revolves
at 1,800 r.p.m. The limiting time of exposure is about 10 minutes, and
in order to reduce the dead time during reloading, special automatic
mechanisms are introduced which stop the rotating shutter after each
exposure, turn the telescope for reloading, and then reset to a prearranged
hour angle for the next exposure. Owing to the position of the film, re¬
loading can only take place by separating the optical system. This is
then reset automatically to within a few ten-thousandths of an inch.
According to reportsf the first of the Super Schmidts to be completed
by the Perkin-Elmer Corporation was installed at Soledad, New Mexico,
during the summer of 1951. Estimates of the relative performance of
these Super Schmidts compared with other meteor cameras have been
made by Whipple J as in Table 7.
Table 7
Characteristics and Performance of the Meteor Cameras
Camera
Aperture
(in.)
Focal
ratio
Number
of
elements
Number
of air
glass
surfaces
Number
of
mirrors
Field
diameter
(deg.)
Light trans¬
mission
taking
Ross Xpres
as unity
Perfor¬
mance
meteors per
100 hours
Ross Xpres .
Cooke-Taylor
3-in. Rosa .
Aerial night
lenses
Classical
Schmidt .
Super
Schmidt .
15
1-6
30
30
180
12 0
4
8
7
2 6
10
007
6
3
4
7
2
6
6
6
8
8
2
10
0
0
0
0
1
1
60
33
20
46
20
50
10
M
08
04
1-4
13
10
0-3
0-7
2-3
20
260
The performance figures for the last three cameras listed in Table 7
are estimated. Allowing for the increased dead time due to the more
frequent film-changes required—every 6 minutes instead of 1 or 2 hours
for the Ross Xpres—Whipple§ estimates that the yield per annum for
the Super Schmidt should be increased by about forty times over the
older cameras. The limiting magnitude is expected to be + 3 or -f 4
instead of — 1 to 0 with the Ross Xpres.
(e) Reduction of Data from the Photographic Plates
The methods used in the Harvard work for obtaining the meteor path
and velocity from the segmented trails on the photographic plates are
described in Chapter XI. It is therefore only necessary in this section
t Sky and Telescope, 10 (1951), 219.
x Whipple, F. L., Tech. Rep. Harv. CoU. Obs. (1947), no. 1.
§ Whipple, F. L., Sky and Telescope (1949), loc. cit.
J/Tii'lU & Kashmir library,
„ 53 VISUAL AND PHOTOGRAPHIC TECHNIQUES
. “ problem in connexion with the contemporary Harvard «ork. In
Ihis woi the brightness of meteors was measured by com P a ™°"'
emulsion against emulsion, with trailed-star images on ungmded plate
taken with the same instrument and the same focal ratio as the meteo
nlate The traded comparison plates, centred on equatorial regions n
fSigS"tars, were JL around culmination with an exposure t,m
of 20 minutes. Two guided plates, each with an exposure time of 00
minutes and centred on the same region, were taken, one before and one
after the traded comparison plate. If no appreciable differences in the
densities of the star images could be detected on the two guided plates,
the series of two guided and one, or more, trailed plates taken in between
was considered satisfactory for photometric purposes.
A number of stars over a range of three to five magnitudes were selected
near the centre of the meteor plate, and their apparent brightness was
compared with that of stars near the centre of the guided comparison
plates. The magnitudes thus obtained for stars on the meteor plate
generally differ by some constant amount Am from the catalogued
magnitude. Am (which we assume to be catalogue magnitude minus
observed magnitude) represents several factors arising from the differ¬
ences in the conditions under which the meteor and comparison plates
were obtained, such as differences in (i) exposure times, (ii) sky trans¬
parency, (iii) plate sensitivity, (iv) differential extinction. Difference
(i) can be easily taken into account. If t ra and t 0 represent the exposure
times of the meteor plate and comparison plate respectively, then
Am = Am—klog 7 -
t 0
represents the correction that has to be applied to meteor magnitudes
because of the combined effects of (ii), (iii), and (iv). k is a coefficient
which allows for the reciprocity law failure (k = 2-2 for the Cramer
high-speed emulsions considered by Jacchia). The magnitude of the
meteor at different points of the trail is obtained by comparison with
the trailed-star images near the centre of the unguided comparison plate.
f Sytinskaya, H. N., Astr. J. U.SJS.R., 12 (1935), 174.
J Millman, P. M., and Hoffleit, D., Ann. Harv. Coll. Obs., loc. cit.
§ Jacchia, L. G., Tech. Rep. Harv. CoU. Obs. (1949), no. 3
22 OBSERVATIONAL METHODS—I II, § 3
Two further correction factors are necessary to the meteor magnitudes
determined in this manner:
(a) A field correction to allow for the dimming of the trails at increasing
distances from the plate centre. Jacchiat gives full details of this
correction, made by comparison with the trailed plates. The corrections
are considerable, as will be seen from Table 8, which gives representative
values for the Harvard AI and FA cameras.
Table 8
Field Correction for the Harvard AI and FA Cameras
Distance from
centre (r cm.)
Correction in magnitudes
AI camera
FA camera
0
0
0
2
-005
-0 04
4
-0-22
-0-21
0
-0-60
-0-52
8
-1-32
-1-22
10
-2-4
-1-52
(P) A velocity correction to allow for the different trailing velocities
of the meteor and the comparison stars. If V mot and V Btar are the trailing
velocities (in mm./sec.) of the meteor and the comparison star respec¬
tively, this correction is given by
f(v) = —2-5 log 55=!*.
V 8Ur
The average velocity of the meteors is about 1,000 times that of the
comparison stars, hence the reciprocity law failure of the emulsion has
to be considered. Jacchia shows that for the Cramer high-speed emulsion
used with the AI and FA cameras a satisfactory expression which takes
account of the reciprocity law failure is
f(v) = -2-657 log Jss*.
V sUr
In the case of meteor trails recorded with unguided cameras, the
photometric measurements can be made by comparison with the trailed
star images on the same plate. The only corrections necessary are the
velocity corrections (P) above, and one to allow for the dimming effect
of the shutter on the star trails. Finally the magnitude has to be reduced
to the standard distance of 100 km. as described in § 1 (c). Jacchia
also introduces a colour correction of +l-8 m for comparison with visual
magnitudes, but until more is known about the colour index of meteors
this latter correction is somewhat arbitrary.
f Jacchia, L. G., 1949, loc. cit.
Ill
OBSERVATIONAL METHODS II
THE HISTORY AND FUNDAMENTAL FEATURES OF
RADIO-ECHO OBSERVATIONS
Intro duc,ion: History of the radio-echo observation of
The radio-* cho techniques for the study of meteors are derived Meetly
layers by using continuous wave-frequency modulat.on techniques and
he atter by using the pulse technique. The mam features of the
ionizecTregions are now very well known, and here it is only necessary to
mention that under normal conditions the electron density in the E
region is subject to a marked solar control reaching a " u m ^noon
and a minimum during the night. For example, ^ Great Br tam at
noon on a summer day the density in the E region .s about 10 electrons
per c.c., decreasing to about 8x 10» electrons per c.c. by rn.dn.ght, the
critical radio-wave frequencies being 3 mc./s. and 0-8 mc./s.
Abnormal effects,? indicated by sudden mcreases in the electron
density of the E region during the night, were reported by many of the
early workers on the ionosphere, notably by He.sing,|| Eckersleytf
Appleton It Appleton and Naismith,§§ and by Schafer and Goodall.||||
Heising described his results as indicating that 'great masses of electrons
are tossed into the atmosphere rather quickly’, while Appleton concluded
that ‘either the recombination of ions is prevented or there is some
ionizing agent present which can influence the dark side of the earth .
Thus by 1930 it had become clear that although the sun was the main
f Appleton, E. V.. and Bamott, M. A. F. f Nature, 115 (1925), 333; Proc. Roy. Soc.
A ^Brort, O., and Tuve, M. A., Terr. Magn. Atmos. Elect. 30 (1925), 15; Nature, 116
(1925), 357; Phys. Rev. 28 (1926), 554.
5 A survey of tho work on ionospheric abnormalities, especially with regard to
meteoric ionization, has been given by Lovell, A. C. B., Rep. Phys. Soc. 1 rog. Phys. II
(1948), 415.
II Heising, R. A., Proc. Inst. Radio Engrs. 16 (1928), 75.
tt Eckersley, T. L., J. Instn. Elect. Engrs. 67 (1929), 992.
tt Appleton, E. V., Proc. Roy. Soc. A 126 (1930), 542.
§§ Appleton, E. V., and Naismith, R., ibid. A 137 (1932), 36.
HI] Schafer, J. P., and Goodall, W. M., Proc. Inst. Radio Engrs. 19 (1931), 1434.
24 OBSERVATIONAL METHODS—II III, § 1
influence in controlling the ionization of the E region, some other ionizing
agency must also be at work.
The suggestion that meteors might cause sufficient disturbance in the
E region to affect the propagation of radio waves appears to have been
made first by Nagaoka.t He considered that a meteor would sweep
away the electrons in its path, and although it would ionize the air
itself the number of electrons produced would be small compared with the
number present before the passage of the meteor. Thus, in the track
of the meteor there would be fewer electrons than in the surrounding
air, and this would cause abrupt changes in the refractive index for an
incident radio wave.
In 1931 SkellettJ suggested that the actual ionization due to meteors
might affect the conditions in the E region, and he pointed out that
Heising’s results might be explained in this manner. Skellett’s theoretical
estimates of the amount of ionization produced by meteors, which he
developed further in 1932,§ were based on the theory of Maris|| and are
now known to be seriously in error.tt Nevertheless, the experimental
work carried out by Schafer and GoodallJJ during the Leonid shower
of 1931, and by Skellett§§ in conjunction with Schafer and Goodall,
produced conclusive evidence that meteoric ionization was responsible
for some of the night-time E region abnormalities. These workers used
the pulse method and observed on frequencies between 1-6 and 6-4
mc./s. in rapid succession. During the 1931 Leonid shower very dis¬
turbed conditions were found in the E region, with sudden abnormal
increases of ionization, reaching a peak on the night of November 16-17,
which was known from visual observations to be the maximum of the
shower. Unfortunately magnetic disturbances were also present on
these nights and hence it was not possible to decide definitely that the
effects were due to meteoric ionization. During the Leonid shower of
1932, however, successful visual correlations of meteors passing overhead
with sudden transient increases in E region ionization were obtained.§§
Figures 5 and 6 show these sudden increases in ionization correlated
with the passage of meteors for the nights of 1932 November 14-16
t Nagaoko, H., Proc. Imp. Acad. Tokyo, 5 (1929), 233; Set. Pap. Inst. Phys. Chem.
Res., Tokyo, 15 (1931), 169.
x SkeUett, A. M., Phys. Rev. 37 (1931), 1668.
§ Skollett, A. M., Proc. Inst. Radio Engrs. 20 (1932), 1933.
|| Maris, H. B., Terr. Magn. Atmos. Elect. 34 (1929), 309.
ft Horlofson, N., Rep. Phys. Soc. Progr. Phys. 11 (1948), 444.
tt Schafer, J. P., and Goodall, W. M., Proc. Inst. Radio Engrs. 20 (1932), 1131; ibid.,
p. 1941.
§§ Skellott, A. M., Proc. Inst. Radio Engrs. 23 (1935), 132.
25
III, §1
RADIO-ECHO OBSERVATIONS
Id 15-16 During nights when no meteor showers were active these
2 oVs o *c a
E ST
Fio. 6. Transient increases in ionization of the E region associated with
meteors passing overhead obtained by Skellett, Schafer, and Goodall on
1932 Nov. 15-16.
From this work the following conclusions were made: (a) night-time
increases in E region ionization were most marked during meteor showers,
(6) for all major increases of ionization a meteor was observed to pass
nearly overhead, (c) the intermittent reflections, lasting only for a period
of seconds, were rare except during meteor showers, ( d ) observations
of the critical frequency gave the ionization in the E region as 10 6
26
OBSERVATIONAL METHODS—II
III. § 1
electrons per c.c. during the maximum of the Leonids, i.e. greater than
its noon value on a summer day.
In Japan, Minohara and Itof also investigated the effect of the 1932
Leonid shower. They found a large increase in the number of short-
duration echoes during the shower, but do not appear to have associated
specific echoes and meteors. Previous to this work QuackJ and Pickard§
Fio. 7. Electron content of the E region during the 1933 Leonid shower os
observed by Mitre, Syam, and Ghose.
investigated the disturbances on long-distance short-wave transmissions
to see if any connexion with meteoric showers existed. Both investigators
found correlations, but in view of the sensitivity of such transmissions
to magnetic disturbances their analysis cannot be regarded as conclusive.
This work during the Leonid shower of 1932 was followed up in India
during the 1933 Leonid shower by Mitra, Syam, and Ghose.|| Their
results for the electron density in the E region during the nights of
1932 November 13-14 and 16-17 are shown in Fig. 7. The electron
densities reached values of 3-3 X 10 s and 2-2 x 10 s per c.c. respectively. The
period was clear of magnetic and solar disturbances. Similar measure¬
ments were made by Bharff during the 1936 Leonid shower.
This early work was followed, during the next few years, by many
studies of these transient increases in the ionization in the E region, and
although several suggestions were made as regards their association
with meteors, no specific relation seems to have been established. For
t Minohara, T., and Ito, Y., Rep. Radio Res. Japan, 3 (1933), 116.
t Quick, E., Elekt. Nachr.-Tech. 8 (1931), 46.
§ Pickard, G. W., Proc. Inst. Radio Engrs. 19 (1931), 1166.
|| Mitra, S. K., Syam, P., and Ghose, B. N., Nature, 133 (1934), 633.
ft Bhar, J. N., Nature, 139 (1937), 470; Indian J. Phya. 11 (1937), 109.
in §1 RADIO-ECHO OBSERVATIONS 27
ftmmSM
from clouds of ions in the E region but did not discuss their orig _
SkellettS emphasized that these results strongly suggested a meteor
origin Appleton and Piddington|| also made detailed measuremen s
o„ S the transient echoes and concluded that the scattering centre
consisted of clouds of 10“ electrons concentrated in a region of linear
dimensions small compared with the wave-length (whichm <their■case
was about 30 m.). It was suggested that these results implied the entry
into the atmosphere by day and night of an agency producing bursts of
ionization. Similar measurements on the transient echoes were made by
Watson-Watt, Wilkins, and Bowenft m 1937 and by Harang« m 1942
In 1938 Pierce§§ made calculations which showed that the ionization due
to meteors could maintain the E region ionization at its day-time value
during the night. His calculations are now known to be in error by several
orders of magnitude, however. In 1940|||| he repeated the observations
of SkeUett, Schafer, and Goodall by observing the echoes on a pulsed
3 mc./s. equipment during the 1940 Leonid shower.
The measurements on the transient signals described above were
made either directly, using pulse technique, or by observations of
scattering into the skip zone when the wave frequency was high enough
to penetrate the normal E region but was reflected from the F region.
A third type of phenomenon can also be caused by the occurrence of
transient clouds of dense ionization in the E region—the scattering of
radio signals to great distances in cases where the frequency is such that
both E and F regions are penetrated and the signal is not normally re¬
ceived above the range of the ground ray. Taylor and Y oungftt reported
abnormal scattering effects whereby high-frequency radio signals were
received at a distant station after traversing a very long path. In 1931
t Appleton, E. V., Naismith, R., and Ingram, L. J., Phil. Trans. 236 (1937),
191.
t Eckersley, T. L., J. Instn. Elect. Engrs. 71 (1932), 405; 86 (1940), 548.
§ Skellott, A. M., Nature, 141 (1938), 472.
|| Appleton, E. V., and Piddington, J. H., Proc. Roy. Soc. 164 (1938), 467.
tt Wateon-Watt, R. A., Wilkins, A. F., and Bowen, E. G., ibid. 161 (1937), 181.
XX Harang, L., Oeofys. Publ. 13 (1942), no. 4.
§§ Pierce, J. A., Proc. Inst. Radio Engrs. 26 (1938), 892.
HU Pierce, J. A., Phys. Rev. 59 (1941), 625.
ttt Taylor, A. H., and Young, L. C., Proc. Inst. Radio Engrs. 16 (1928), 561; 17 (1929),
1491.
28
OBSERVATIONAL METHODS—II
III. § 1
Beverage, Peterson, and Hansellf found occasional signals at very great
distances on frequencies as high as 40 mc./s. In 1933 JonesJ observed
bursts of signals up to 200 miles from transmitters working on frequencies
in the range 36 to 100 mc./s. with occasional maxima of great intensity.
In 1938 Pierce§ discussed this type of phenomenon and pointed out that
such bursts could be caused by meteor ionization. In 1942-4 workers
of the Federal Communications Commission Engineering Department,||
using transmitters in the frequency range 42 to 84 mc./s., and observing
at distances of 100 to 340 miles, investigated these bursts in detail;
visual correlation of the bursts with meteors was obtained on several
occasions during 1944 August and November. The diurnal variation of
numbers of bursts (Fig. 8) shows good agreement with the theoretical
and experimental data on the diurnal variation in numbers of meteors.
These workers observed that on 71-76 mc./s. the bursts were less frequent
and of shorter duration than on 44 mc./s.
It will be seen that a large amount of evidence steadily accumulated,
indicating that the entry of meteors into the atmosphere gave rise to
transient increases of ionization which could be observed as short-lived
echoes on suitably pulsed radio equipments. It was not until after the
Second World War, however, that the radio techniques were deployed
in the specific study of meteoric phenomena. The development of radio
transmitters and receivers during the war, working on frequencies
considerably in excess of the critical E and F region frequencies, gave a
great impetus to the study of the transient meteoric echoes.
The work of Hey and Stewartft. tt in 1945 and 1946 and of Prentice,
Lovell, and Banwell§§ in 1946 showed conclusively that with suitable
equipment a close correspondence existed between the radio echoes and
meteors. For example, Fig. 9 shows the mean hourly rate of occurrence
t Beverage, H. H., Peterson, H. O., and Hansel], C. W., Proc. Inst. Radio Engrs. 19
(1931), 1313. X J° nea » L. F., ibid. 21 (1933), 349.
§ Pierce, J. A., 1938, loc. cit.
|| Federal Communications Commission; Engineering Dept. Docket (1944), no. 6651,
tf Hoy, J. S., and Stewart, G. S., Nature, 158 (1946), 481; Proc. Phys. Soc. 59 (1947), 858.
ff This work arose directly from observations made by Army G.L. Mark II radar
equipments during the V2 rocket attacks on London in the latter part of 1944. Thoso
equipments were used to detect the approaching V2’s in order that early warning could
be given; but many echoes at the appropriate range were observed when no V2's had
been launched. An analysis of theso echoes was published as a secret memorandum
(No. 462) by the Army Operational Research Group. The work immediately after the
end of the war which confirmed their relationship with meteors was described in a
further report (No. 348) by Hey and Stewart. Observations of the echoes made by the
coastal radar chain in the British Isles were described by Eastwood, E., and Mercer,
K. A. (Proc. Phys. Soc. 61 (1948), 122).
§§ Prentice, J. P. M., Lovell, A. C. B., and Banwell, C. J., Afon. Not. Roy. Astr. Soc.
107 (1947), 155.
of echoes observed by Hey and Stewartf in 1946 January to June with a
pulsed apparatus on a wave-length of 5 m. The peak in the hourly rate
in January corresponds to the Quadrantid meteor shower and that m
April to the Lyrid shower, both agreeing in time with the visible occur¬
rence of these showers. Similar curves of the activity during the summer
of 1946 including the Perseid shower were obtained by Prentice, Lovell,
and Banwell.J The very much more striking events observed during the
great Giacobinid shower in October of that year are described in Chapter
XVI. During this period several groups of workers in America, Canada,
t Hey, J. S., and Stewart. G. S., Nature, 158 (1946), 481; Proc. Phys. Soc. 59 (1947),
86 j prentice, J. P. M., Lovell, A. C. B., and Banwell, C. J., Mon. Not. Roy. Astr. Soc.
107 (1947), 155.
30
OBSERVATIONAL METHODS—II
HI, §1
and Great Britain developed these radar and radio techniques for the
study of specific problems in meteor astronomy and meteor physics.
Some of the basic techniques are described in the remaining sections of
this chapter, and the many results obtained in recent years are discussed
in the appropriate later chapters of the book.
•O 20 SO 10 ZO JO 10 go JO
April May June
Fio. 9. Mean hourly rato of occurrence of radio echoes observed by Hoy end
Stewart in 1946.
2. Contemporary radio techniques for the study of meteors
(a) Introduction
The essential units in a radio apparatus for the study of meteors are
the transmitter, receiver, aerial system, and display unit or recorder.
The transmitter may generate either pulsed or continuous wave (c.w.)
signals. In the former system the transmitted pulses are usually of the
order of 10 microsec. in duration, and are radiated at a recurrence rate
which generally lies between 50 and 1,000 pulses per second, depending
on the particular problems under investigation. After scattering by the
ionized meteor trail the returned pulses are received and can be most
readily observed by displaying as an echo on a cathode-ray tube display
with a linear time base, the commencement of which is synchronized
with the transmitter pulse. On account of this synchronization the
sequence of scattered pulses appear as an echo at a fixed point on the
nI §2 RADIO-ECHO OBSERVATIONS
- - f B -'»«?"
Fia. 10. The pulsed method of observing meteor trails.
Fio. 11. The continuous-wave frequency modulation method.
can be measured accurately from the separation of the ground and echo
pulses on the cathode-ray tube time base, and hence R can be determined
readily.
If the transmitter radiates continuous waves, then it must be frequency
modulated in order to determine ranges. This is illustrated in Fig. 11,
where the transmitter frequency increases linearly from f x to f 2 in time
r 0 . The wave returned from the meteor trail will be delayed by a time
t = 2R/c: hence at a given instant the transmitted and received signals
differ in frequency, and interference beats will be observed at the receiver
output as indicated in the lower diagram of Fig. 11. The beat frequency
32
OBSERVATIONAL METHODS—II
III, §2
is clearly given by
-<W»> =
T o c
The total number of beats in one frequency sweep is therefore —(fj—fj)
and hence the range is determined by counting the number of beats in
each sweep.
It can be shown that for a given mean transmitter power, and other
parameters constant, there is no difference in either pulse or frequency
modulated systems as far as sensitivity and accuracy of range measure¬
ment are concerned. The pulse method has certain advantages in
display, especially when the signals are scattered at the same time from
more than one object. As far as meteor work is concerned the pulse
method has been used almost exclusively in the applications requiring
a range measurement. In fact it is difficult to find cases where the fre¬
quency modulation technique has been applied to meteor observation.
On the other hand, as will be seen later, the continuous wave methods,
without frequency modulation, have been extensively used for the
determination of meteor velocities. In this case an auxiliary pulsed
system is necessary to give the range of the meteor trail.
The basic circuits and techniques which are used in contemporary
transmitters and receivers are largely identical with those applicable
to radar. These are adequately described in the many texts devoted to
radarf and it would be inappropriate to enter into details in this book.
The factors governing choice of transmitter pulse width, receiver band
width, aerial parameters, display systems, and wave-length are often
different, however, when such equipment is used in the study of meteors.
A brief discussion of some relevant points follows.
(6) Pulse Width and Band Width
The choice of transmitter pulse width and receiver band width for a
meteor equipment depends on the various interdependent factors
f Tl»© following, amongst a large solection, may be recommended as filling in the
background to this chapter.
All books in the Cambridge 'Modern Radio Technique’ series, especially Taylor, D.,
and Westcott, C. H., Principles of Radar ; Smith, R. A., Aerials for Metre and Decimetre
Wavelengths ; Moxon, L. A., Radio Receivers for Metre and Decimetre Wavelengths.
The chapter on ‘Radar’ by Smith, R. A., in Electronics (edited by Lovell, B.), Chapman
& Hall.
Full accounts of radar techniques by many of the original workers are given in the
special Radiolocation volume of the J. Instn. Elect. Engrs. (93 IHa, 1946), and also by
the Radar School Staff at the Massachusetts Institute of Technology in Principles of
Radar (McGraw-Hill). A complete account is also given by Ridenour, L. N., Radar
System Engineering (McGraw-Hill, 1947).
nI 5 2 RADIO-ECHO OBSERVATIONS
common in radar applications. In the latter the choice is mainly govern^
by consideration of range discrimination, range accuracy “T
In the meteor case the question of discriminatmn is not usuaUy sign*
cant. For example, with a pulse length of 10 m.crosec. two ob ects
separated by 1 km. could be resolved. Apart from certain specialized
techniques in the field of meteor physics S u ch h .gh dl s cr .m,nation
unnecessary, and the pulse length can therefore be determined by other
considerations.
The pulse of transmitted radio frequency energy has a fiequen y
spectrum spread around a mean value, which is the radio frequency of
the transmitter. Ideally the receiver is required to pass this pulse
without distorting it. Thus, in principle, the receiver should be able
to pass the band of frequencies comprising the pulse spectrum, bince
the pulse spectrum comprises an infinite range of frequencies this would
entail a receiver with an infinitely wide pass band. In practice a com¬
promise is made between finite band width and distortion of the pulse.
According to Fourier’s theorem a periodic function <l>(t) repeating
in time t 0 can be expanded in harmonic terms
D(t) = k+ 2 acos ( ? v) + 2 b8in ( ? v)'
The recurrent function is therefore an infinite series of harmonic oscilla¬
tions of frequency n/t 0 , where n is a positive integer. The full analysis of
the spectrum of a train of pulses (as distinct from the spectrum of
sinusoidal modulation), is somewhat complex and need not concern us
here.t It is sufficient to note that the spectrum consists of a series of
lines separated by the intervals between successive transmitted pulses
(recurrence frequency f 0 = l/t 0 ) as indicated in Fig. 12. The amplifies-
tion of such a pulse sequence without distortion would require a receiver
with an infinitely wide band width. It is evident from Fig. 12 that most
of the spectrum is contained within a frequency band of the order 2/r.
It can be shown that r corresponds to the width of the transmitted pulse,
and in the practical design of receivers a band width of about 1/r is
usually taken as the best compromise. It leads to a rounding of the pulse
shape as shown in Fig. 13. The degree to which such rounding can bo
tolerated depends on the range accuracy required, since accurate
ranging requires the transmission of a steep-fronted pulse and the
maintenance of the steep front through the receiver. In the example
f A detailed discussion of tho appropriate Fourier analysis for the cose of pulsed
transmission and reception is given by Lawson, J. L-, and Uhlonbeck, G. E., in Threshold
Signals, McGraw-Hill, 1950.
8505.06 D
34
OBSERVATIONAL METHODS—II
III. §2
shown in Fig. 13 the limit of accuracy of the range measurement will be
set by the time interval P'Q'. If it is required to measure the range of a
meteor trail to ±10 km. then this time interval must not be greater
than 2AR/C ~ 6-6 microsec. If the receiver affects the pulse shape as
shown in Fig. 13 (which approximates to the practical case of band width
Fio. 12. Frequency spectrum of a sequence of pulses of recurrence frequency
. f.(- 1/t,).
Fio. 13. Square-toppod transmitted pulse (a) of length r, and (6) the approxi-
mate shape of the pulse when passed through a receiver with band width 1/r.
~ 1/t), then the pulse width should also be about 6-6 microsec.; and
hence the optimum receiver band width ( 1 /r) about 150 kc./s. If greater
range accuracy is required the receiver band width must be widened in
order to increase the sharpness of the front of the pulse; but this will
increase the noise level without increasing the pulse amplitude, and sen¬
sitivity will be lost. Conversely, if the receiver band width is decreased
below the optimum value of 1/r, the pulse shape will not only be more
rounded but the amplitude of the pulse will be reduced. Hence although
the noise level is decreased there will be no increase in sensitivity, and
the accuracy of range determination will be worsened.
Of course, the same result could be obtained by, for example, using a
pulse length of 66 microsec. and a band width of 15 kc./s. In normal
radar applications this would be inadmissible because range discrimina¬
tion would be no better than about 10 km., but in meteor work this would
OIJ
XII §2 RADIO-ECHO OBSERVATIONS
not normally be a drawback. In fact, the over-all sensitivity off the
system to meteor trails would be improved because of the reduction of
receiver noise by virtue ofthe narrower band width. In P ract '^^'
ever, a limit is often set to such increases in pulse width because
transmitter power limitations. The benefit of increased sensitivity
would only be obtained provided the peak power m the transmitter
pulse remained constant, which for a given recurrence frequency would
entail a tenfold increase in mean power. The mean power cou d be
reduced by decreasing the recurrence frequency. It will be seen later,
however, that the attainment of the utmost sensitivity is not an urgent
problem in meteor astronomy, and that the requirements of velocity
determination demand high recurrence frequencies, which in turn
demand that the pulses should be short because of mean power limita¬
tions in the transmitter.
The result of these various criteria is that for the study of problems in
meteor astronomy the pulsed radio equipments generally have trans¬
mitters radiating pulses of about 10 microsec., at a recurrence rate
of a few hundred per second. Peak powers in the pulse generally range
from about 5 to a few hundred kilowatts, but the mean powers are, of
course, generally less than 1 kilowatt. Sufficient accuracy of range
measurement is generally obtained when the receiver band width is
adjusted in relation to pulse width as discussed above—in this case
about 100 kc./s.
Although not of direct interest to meteor observations, it may be
mentioned that in the case of the continuous wave techniques similar
considerations apply. The range accuracy then depends on the beat
frequency and the time of observation (Fig. 11). It is easy to show that
the accuracy is of the order of the reciprocal of the receiver band width;
and that for similar transmitter mean powers the over-all sensitivity of
pulse and continuous wave equipments is identical. Actually, as men¬
tioned earlier, the continuous wave techniques are not normally used
in meteor work for range measurements. They are, however, widely
used for meteor velocity measurements (see Chapter IV). The receiver
band width requirements are then determined by the modulation fre¬
quency caused by the Fresnel zone oscillations during the formation
ofthe meteor trail, which amounts to a few hundred cycles per second.
(c) Aerial Systems
A wide variety of aerial systems have been used for transmission and
reception in meteor work. For some applications a wide coverage is
36
OBSERVATIONAL METHODS—II
III, §2
desirable; in others high directivity is required. The principles and
practice in the design of these aerials have followed closely those used
in the radar applications^ and here it is only necessary to refer to one or
two general concepts. As a consequence of the reciprocity theorem the
properties of an aerial may be regarded as identical whether it is in
use for the transmission or reception of radio energy.
If the transmitter is connected to a system radiating a power P iso¬
tropically, then the power density at a distance R will be P/47 tR 2 .
Any practicable aerial system will have a power gain G over an iso¬
tropic source, where G is defined such that the power density in a given
direction is GP/47 tR 2 . The power gain G as normally used refers to the
gain in the direction of maximum radiation. The power density in any
other direction is obtained from the polar diagram of the aerial system
f (9, <f>), where 9 and (f> are the angles from the direction of maximum radia¬
tion in two planes at right angles. At a distance R in any direction
(0, <f>) the power density will be W o f*(0, (f >), where W 0 is the power density
in the direction of maximum radiation. The total flux of power from
the aerial will be fj W 0 P(9 t (f>) dto, where da t is the elementary solid
angle and, by definition, this must be 1/G times the flux from an iso¬
tropic source radiating with a power density equal to that at the maxi¬
mum. Hence we reach the general result that
G JJ f*(M) d<« = 4*. (1)
The most elementary form of radiator is the Hertzian dipole, an
electric doublet with dimensions small compared with the wave-length.
All current elements in the dipole are in phase and the polar diagram is
given by f(0) = cos 6 (Fig. 14). Thus, applying (1),
\n 2 rr
G J I COS 3 0 d 9d<f> = 47r,
or G = 1-5.
The simplest possible aerial system therefore has a power gain of 1*5
over the idealized isotropic radiator.
On the comparatively short wave-lengths which are mostly used in
the radio investigation of meteors, the elementary form of radiator is
more often the centre-fed half-wave dipole (Fig. 15). This dipole has a
natural resonant frequency corresponding to a wave-length of twice its
length, and if driven at this frequency it radiates strongly with a polar
f The books listed on p. 32 contain accounts of radar aerials.
III. §2
RADIO-ECHO OBSERVATIONS
in 2 n
•JJ
0
cos^frsing )^,, dgd , = 4w>
cos 2 0
or
The power gain of the half-wave
is therefore 1-09.
G = 1-635.
dipole over that of the Hertzian dipole
Fia 14. Radiation from the Hertzian dipolo in the plane
of the electric vector. In tho piano at right angles tho
radiation is constant with
i
i
I
I
l
A /«
i
!
i
»
Fio. 15. Half-wave dipole and its radiation in the piano of tho electric vector
compared with tho radiation from a Hortzian dipolo. In tho piano ut right
angles tho radiation is constant with
Unfortunately there is no universally accepted standard as to w hether
the power gain of an aerial system is expressed in terms of gain over an
isotropic radiator, Hertzian dipole, or half-wave dipole. The expressions
of power gain either in terms of an isotropic radiator or half-wave dipole
are most commonly encountered, the latter being convenient in experi¬
mental work since the half-wave dipole is the fundamental driving
element of most aerial arrays.
The simple half-wave dipole is a common aerial used for transmission
and reception where wide coverage is required. In many applications
much more highly directive aerial beams are required (for example, in
the determination of meteor radiants described in Chapter IV). One
38
OBSERVATIONAL METHODS—II
HI, §2
common method of achieving directivity is to feed the transmitter
power into a number of elements, and by appropriate phasing to arrange
for reduction of radiation in certain directions with consequent increase
in others. For example, suppose the transmitter power is fed to n equally
spaced elements in a row as in Fig. 16, each element of which has a polar
Fio. 16. Radiation from a linear array of n equally
spaced element*.
diagram f(0). If the rth element has current i r and phase then the
field at (R r 6) from this element will be
E r =
where k is a constant and A the wave-length. From the whole aerial
E = kf(0) r £
r-l
If d is the element spacing R r = R x -f (r— l)dsin0, and for the same
current in each element and for zero a’s summation gives
Maximum radiation occurs for 6 = 0 and zeros when sin 6 = NA/nd
(N = 1,2,3,...). For spacing d of less than A there is one principal maxi¬
mum and a series of side lobes as shown in Fig. 17. The radiation of the
main lobe falls to zero at sin0 = A/nd: but if the total aperture of the
aerial (n—l)d >A, this reduces to 9 = A/a, where a is the over-all
dimension of the aerial.
The above is a simple example of a linear array producing directivity
in one direction (0). If directivity is also required in the plane at right
angles {</>), then a series of such linear arrays must be placed side by side
to form a broadside array. In 1928 a Japanese engineer Yagi devised
an alternative form of directive aerial in which only the half-wave dipole
39
radio-echo observations
is fed, but which has been widely
sitic directors as indicated in g. • easier to construct
—-—-
F:o. 18. Form of Yagi aerial for producing a directive beam.
lobes. The details of such broadside arrays and Yagis are given in many
of the standard texts referred to previously.
The other main form of aerial used for obtaining directivity is the
paraboloidal aerial, in which a half-wave dipole or smaU array is mounted
at the focus of a parabolic surface in order to produce a uniform phase
field across its aperture. One great advantage of this type of aerial is
that the wave-length can be readily changed by adjusting the dipole
feed system. If in Fig. 19 the curved surface is paraboloidal and the
aperture rectangular with the focus in the aperture plane, the radiated
field can be obtained as follows. Let E(x) be the field (in amplitude and
phase) at a point in the aperture plane at a distance x from the edge of
40
OBSERVATIONAL METHODS—II
III, 5 2
the mirror. Then, by Huygens’ principle, the field at a distant point can
be obtained by summing the contributions from each element of the
aperture with the appropriate phase relationship, giving
E(0) = k j E(x)e« I ”i“ , ° dx, ( 2 )
the integral being taken over the aperture.
Fio. 19. Radiation from a paraboloidal aerial system.
For uniform phase and amplitude distribution across the aperture
(2) gives the polar diagram as
(tt d'sinlA
“bn
E (0) = const
tt d'sinfl
where d' is the length of the aperture.
If d' > A, the first zero occurs at 6 ~ A/d'.
A similar expression will be appropriate in the <f> plane. Thus for a
rectangular aperture of sides d', d", the first zeros in the principal planes
will occur at A/d', A/d" and the power will be effectively concentrated
in a solid angle A 2 /d'd*. Then the power gain of the paraboloid will be
4tt d'd*
A 2
In the case of a full paraboloid with circular aperture of radius a 0 ,
uniformly illuminated, the beam will have circular symmetry. The polar
diagram can be shownf to be given in terms of the first-order Bessel
E <"> - T^ifr 1 ' < s >
f See, for example, Slater, J. C., Microicavc Transmission, McGraw-Hill, 1942.
Ill, §2
RADIO-ECHO OBSERVATIONS
41
G =
4?rA
and the power gain
where A = waj is the area of the aperture. The first zero from (3) occurs
at 9 = 1-22AK, where a; (= 2a 0 ) is the diameter of the aperture. The
beam from the uniformly illuminated circular aperture .s therefore
1-22 times wider than that from the uniformly illuminated rectangular
aperture with side the same as the diameter of the circular aperture.
The field strength of the first side lobe is, however, reduced to 13 per
cent of the main lobe instead of 21 per cent, for the rectangular aperture.
In actual practice it is impossible to obtain uniform illumination of
the aperture: neither is circular symmetry generally achieved because
of tho differing polar diagram of the primary feed source in the two
planes The general result is a broadening of the main beam, diminution
of gain, and reduction of side-lobe intensity relative to the uniformly
illuminated aperture.
The attainment of aerial systems of high directivity which are often
required in meteor work is hindered by mechanical difficulties. The
most useful wave-lengths for meteor work lie in the 3- to 10-metre
wave band. Thus, to produce a beam of width ± 10° to the first zero on
a wave-length of 5 metres would require an aerial aperture of about 36
metres. Such an arrangement can be fairly readily constructed to produce
such a beam in a fixed direction, especially when the beaming is required
only in one plane. On the other hand, if it is required to direct an aerial
the mechanical difficulties become rather severe. One of the largest
directional aerials so far used in meteor work consisted of an array of
five Yagi systems mounted on a large army searchlight base, which gave
a beam of about ±16° to the first zero when used on a wave-length of
4 m.f
In the case of these large aerial structures it is almost always common
practice to use an electronic switching arrangement whereby the same
aerial may be employed both for transmission and reception simul¬
taneously.
(d) Display and Recording Systems
Some form of cathode-ray tube display is used almost universally in
all forms of apparatus for the observation of the radio echoes from meteor
trails. For monitoring purposes the range amplitude display (Fig. 20)
is generally used. The time base sweep C is synchronized with the
transmitter pulse by electronic circuits of the type which are described
t Photographs of this and other aerials used in meteor work have been givon in
Radio Astronomy by Lovell, A. C. B., and Clegg, J. A., Chapman & Hall, 1952.
Fio. 21. Meteor echoes on an inten¬
sity modulated range-time display
(see also photographic reproduction
in Plate I).
past the cathode-ray
f See note on p. 32.
X This topic will not be discussed much in
other similar features in Meteor Physics.
nI §2 RADIO ECHO OBSERVATIONS 43
range duration, and time of occurrence of the echoes is obtained as
sho^ in Fig- 21. This is the type of display used in the apparatus
for determining meteor radiants described in Chapter IV.
f These may be regarded as the two basic types of display used in the
radio-echo meteor work, but special adaptations have been made for
specific purposes. Examples of those used m the work on the velocity
measurements will be described in Chapter IV.
(e) Radio Wave-length and Sensitivity of Equipment—the Fundamental
Radio-echo Equation
The choice of one of the most crucial parameters—the wave-length ol
the radio equipment—remains to be discussed. Originally, as mentioned
in § 1, the transient echoes were observed on equipments designed for
investigation of the ionosphere, and hence operated on wave-lengths of,
say, 20 to 100 m. The pioneer post-war work of Hey and Stewart was
carried out with array equipment which, for operational purposes, had
been designed to work on wave-lengths in the 4- to 5-m. band. It was soon
evident that on these shorter wave-lengths the transient echoes were
much fewer, and were more clearly associated with the visual meteoric
occurrences. However, only since the development of the theory of the
scattering processes has there been any quantitative guide to the
correct choice of wave-length for specific investigations. It is not in¬
tended to discuss these matters in any detail in the present book, but
the deduction of the fundamental scattering equation will make clear
the relations of the wave-length, receiver sensitivity, and other para¬
meters discussed in this chapter. This treatment follows that of Lovellf
and Lovell and Clegg. I
Consider a cluster of N electrons at a distance R cm. from a radio
transmitter and receiver working on a wave-length of A cm. If the size
of the cluster is small compared with A and if the electrons reach their
full velocity under the influence of the impressed e.m.f. and are not
impeded by collisions, then the cross-section for scattering by the
N electrons will be
H^j N2sq - cm -
where e and m are the charge and mass of the electron and c the velocity
of light.
If the peak power in the transmitter pulse is P watts, and if the aerial
t Lovell. A. C. B., Nature, 160 (1947), 670.
x Lovell, A. C. B., and Clegg, J. A., Proc. Phys. Soc. 60 (1948), 491.
44
OBSERVATIONAL METHODS—II
III, §2
system of the transmitter has a power gain G' over an isotropic source,
then the power density at R cm. will be
PG'
477R 2
watts/sq. cm.
The power density of this scattered radiation when it returns to the
receiving aerial will be
J-i- watts/sq. cm.t
3 \mc 2 / 4 ttR 2 4ttR 2
If G' 0 is the power gain of the receiving aerial over an isotropic source
then its effective collecting area will be
Go A 2 /4 tt sq. cm.
and the power delivered to a matched load when situated in a field of
mean power density a will bej
g;a 2
47r
a.
Thus the amount of energy <5 delivered to the receiver after scattering
by the cluster of N electrons will be
- 8 / e 2 \« m 1-5PG' GiA*
OJ = -7T -; XV 8 — watts -
3 \mc 2 / 16 tt 2 R 4 4t r
If we assume that the same aerial is used both for transmission and
reception and express the power gain G in terms of a half-wave dipole,
then G' = G^ = 1-64G and the above expression reduces to
OJ
8 / e* \*
3 \ 1 nc 7
^aS.watts.
If the voltage amplitude at the receiver input is V and the input resis¬
tance r then yt _ 2r ,z;
p _ k —
v - k °w
( 6 )
where
,, 8 /e*\*PG*
The meteor trail consists of a long narrow column of ionization whose
diameter is small compared with A, hence the appropriate number of
electrons to be included in (4) can be calculated by using optical diffrac-
f The factor of 1-5 in this equation arises because the electrons scatter as Hertzian
dipoles and not uniformly through 4w.
X This differs from the equation given by Lovell and Clegg (loc. cit.) which was in¬
correctly stated as GoA*<7/8rr.
RADIO-ECHO OBSERVATIONS
45
III. §2
n theorv The voltage amplitude returned to the receiver from a
Si*Snt of track ^at an angle • to the perpendicular from the
receiver to the trail is given by (5) as
where ou is the number of electrons per cm. path in the trail.
Then the voltage amplitude from the portion of the trail B =
0 = 0, is given by Fresnel’s integral in the form
0 to
Co® 5 V 2 dV + ^p
V 2 dV,
where V = 20^(R/A).
The voltage amplitude at the receiver
due to the whole track is then
and by comparison
given byf
with (5) the appropriate
number of electrons N is
Hence, from (4), the amount of energy at the receiver input due to
scattering from a meteor trail with an electron density of <x 0 electrons/cm.
will be
to =
a% PG 2 A 3
12tt 2 R 3
S’
watts.
( 6 )
The above treatment applies only when the electron volume density
in the meteor column is less than the critical value for the wave-length em¬
ployed. Kaiser and ClossJ have shown that the formula may be applied
to the case of scattering from trails of electron line density less than about
10 12 electrons/cm. when the electric vector is parallel to the trail. When
the electric vector is transverse to the trail, plasma resonances may,
under certain conditions, give a somewhat enhanced return of scattered
power. For electron densities greater than 10 12 electrons/cm. the trail
behaves as a metallic cylinder and it has been shown by Kaiser and
f In this calculation the phase correction is applied twice because of the curvature
of the incident and reflected wave surfaces. The wave-length is then effectively reduced
to A/2, giving N = a # V(AR/2) instead of the more familiar form N = a«V(AR) of optical
theory.
X Kaiser, T., and Closs, R. L., Phil. Mag. 63 (1952), 1.
46
OBSERVATIONAL METHODS—II
HI, §2
Clos8t and by Greenhowj that (6) then becomes
ojPGW/ e* U
lm t?) '
CO =
(?)
20tt 3 R 3 \
The ionized trail will immediately diffuse and when formula (6) applies
the initial signal amplitude V 0 will decrease exponentially to a value V
at time t given byj
F=Fo exp(-l^) > (8)
a * r
where D is the diffusion coefficient. Thus the echo duration for trails
with less than 10 12 electrons/cm. varies as A 2 and does not depend on the
actual density in the trail.
On the other hand, for trails with more than 10 12 electrons/cm. it can
be shownf that the duration AT varies also with a 0 and is given by
AT = conatpA« (9)
When (6) applies the signal amplitude VF provides a direct measure of
the line density a 0 , but in (7) the signal amplitude increases only as the
fourth root of the line density, and for these dense trails the actual
duration as given by (9) provides a more satisfactory measure of the
line density.
The validity of (6), (7), (8), and (9) has been well established experi¬
mentally. These results and their implications will not be discussed in
the present work; it is sufficient to notice:
(а) that the received power <5 varies as P, G 2 , and A 3 for each scattering
mechanism;
(б) that the combined visual and radio-echo observations? show that
a line density of about 10 12 electrons/cm. is produced by a meteor of
about 5th magnitude. Thus the majority of meteors in the range of
visual magnitudes will fall into the high-density category, and formulae
(7) and (9) are appropriate.
The over-all sensitivity of the equipment and the number of radio
echoes obtained will therefore depend directly on the basic receiver
noise level oi 0 , and on P, G 2 , and A 3 . The following are some of the main
considerations governing the choice of these parameters in a practical
meteor equipment.
(i) The basic receiver noise level d> 0 . If an ideal noiseless receiver was
matched to a resistance at its input, then according to Nyquist’s theorem
f Kaiaer, T., and Closs, R. L., Phil. Mag. 63 (1962), 1; Greenhow, J. S., Proc. Phya.
Soc. 65 (1952), 169.
x Herlofson, N., Rep. Phya. Soc. Progr. Phya. 11 (1947), 444.
§ Greenhow, J. S., and Hawkins, G. S., Nature, 170 (1962), 355.
nI §2 RADIO-ECHO OBSERVATIONS
the thermal agitation in the resistor delivers a power kTAfio the receiver,
where k is Boltzmann’s constant, T the absolute temperature of the
resistance, and Af the frequency acceptance band. The noise generated
in the components of any practicable receiver will give rise to an addi¬
tional noise power and the total noise of a receiver matched to a resistance
is generally written as NkTAf,
where N is the noise factor of the receiver and is commonly used as a
measure of the performance of the receiver. At room temperatures
kT ~ 4 X 10 -21 joules, and practicable noise factors with contemporary
techniques vary from about three in the metre wave band to twelve or
more in the centimetre wave band.
In addition to this receiver noise, a receiver connected to an aerial
will also pick up solar and galactic radio emissions which appear with the
same characteristics as the noise generated in the receiver itself. If
this external noise is represented by P„ per unit band width, then the
total noise in the receiver will be
dJ 0 = (NkT+PJAf. (10)
Referring to equations (6) and (7), the signal scattered from the meteor
trail will only be readily detectable if
u> > u> Q .
The common measure of the strength of the returned signal is the ratio
of the amplitude of the signal to the amplitude of the noise, which will
be proportional to
Hence, with the other apparatus parameters in equations (6) and (7)
fixed, the detection of the meteor echo will be determined by the value of
w 0 . Whether the lower limit of u> 0 is determined by the receiver noise
(NkT in (10)), or the galactic noise (P 0 in (10)) depends largely on the
wave-length. As a general guide it may be stated that for wave-lengths
longer than about 3 m. the galactic noise is generally greater than the
receiver noise and this sets the limit to the sensitivity of the receiver.
To a certain extent this can be avoided if special directional arrays are
used to avoid the areas of maximum noise emission in the galaxy. On the
other hand, for wave-lengths less than about 3 m., the receiver sensitivity
is generally limited by the noise generated internally. It will be seen
below that most meteor equipments operate on wave-lengths above 3 m.
and hence the former case applies. w 0 can, of course, be reduced by
decreasing the receiver band width Af, but the limitations here as
regards accuracy of range measurement have already been discussed.
48
OBSERVATIONAL METHODS—II
HI, §2
As regards the actual value of d3 0 if, as an example, we take Af = 1 mc./s.
then kTAf ^ 4 x 10 -15 watts. On a wave-length of 4 m., a noise factor
N of about 3 is readily attainable, giving NkTAf ~ 1-2 x 10~ 14 watts.
If such a receiver was connected to a narrow beam aerial, the galactic
noise on this wave-length would predominate when the beam was directed
at the Milk y Way. For a beam pointed in the neighbourhood of the
galactic centre <D 0 would be limited to somewhere between 10~ 12 and
10~ 13 watts. For a direction away from the plane of the Milky Way it
would, however, be possible to reach a value of d5 0 somewhere near the
above limit of 1*2 X10 -14 watts.
(ii) The peak transmitter power P. According to equations (6) and (7)
the power scattered from the meteor trail increases directly as the peak
transmitter power P. As a guide to what is practicable it may be stated
that peak powers of 100 kw. are fairly readily attainable on the wave¬
lengths under discussion. An increase of ten times over this figure
requires a considerable technological enterprise, and so far in meteor
work, peak powers of 200 to 300 kw. appear to be the maximum yet used.
Whether such values can be attained with a given transmitter depends
on a number of interlocking factors, especially on the pulse width r
and recurrence frequency f 0 , since the mean power W is given by
_ W = Pf 0 r.
In a given transmitter W is generally limited by power supplies and
valve dissipation, and within this limit it is possible to vary P, f 0 , and r
considerably. The factors governing r as regards range accuracy have
already been discussed. For routine observations values of f 0 of 25 or 50
per second are satisfactory, but in certain specialized applications—
such as the determination of velocities—it is necessary to use much higher
recurrence frequencies of 600 or more. In one case where it was necessary
to obtain the maximum over-all sensitivity of the equipment, Almond,
Davies, and Lovellf employed a special device to retain a high peak
power with such a high recurrence frequency. The high recurrence was
required only for the duration of the Fresnel zone pattern. It was there¬
fore arranged that the transmitter normally radiated with a pulse
recurrence of 150, which was switched by an electronic device to 600 as
soon as the first echo pulse was received.
(iii) The aerial power gain G. The factors governing the power gain
G of aerial systems have been discussed in § 2 (c). According to equa¬
tions (6) and (7) the scattered power received from a meteor trail increases
t Almond, M., Davies, J. G., and Lovell, A. C. B., Mon. Not. Roy. Astr. Soc. Ill (1951),
585.
49
in §2 RADIO-ECHO OBSERVATIONS
as G* (assuming the same aerial is in use both for transmission and
reception). It is important to notice, however, that the mam effect of
increasing G is to enable fainter meteors to be detected, and not neces¬
sarily to increase the number detected. It is implicit in (1) that increase
in G means a decrease in beam width, and hence of collecting area. The
actual change in numbers recorded with change of G depends both on
the distribution of meteor radiants and on the mass distribution. In
the case of a uniform distribution of meteor radiants and for the case
where the number N of meteors of mass m is such that the total mass
is constant for each magnitude range, then it can be shown that change of
G will not change the numbers seen, but merely shift the magnitude range
of those which are detected. This particular situation is found in the
sporadic meteor distribution.
However, in many applications—particularly those concerned with
the delineation of meteor radiants, or with the selection of meteors from
a given direction—the width of the beam is the chief criterion. The
actual numerical value of G is therefore not necessarily of chief signifi¬
cance in the design of aerials for meteor work.
(iv) The wave-length A. The wave-length enters in equations (6) and
(7) as A 3 and is therefore the dominant factor as far as numbers of echoes
are concerned. With the type of meteor apparatus readily available
giving peak powers of say 100 kw. and with the best values of w 0 it is
found that very few meteor echoes can be seen on wave-lengths of 2 m.
or less, even during active showers. The most commonly used wave¬
lengths are in the 4- to 10-m. range. The actual choice again depends on
a number of other factors, particularly the requirements regarding
beam width. Mechanical difficulties make directional systems difficult
to achieve on wave-lengths of 8 m. or more, and hence the 4-m. range
has been widely favoured for such applications as radiant determination.
With conventional values of P and di 0 the number of echoes on this
wave-length is found to bear a fairly close relation to the number seen
by a single visual observer under good sky conditions. The 8-m. range
has been used in the experiments on the velocity distribution of sporadic
meteors, both on account of the desire to study the faint meteors and
also because on these longer wave-lengths the time of decay of echo
amplitude (given by (8)) is sufficiently long for the Fresnel zone forma¬
tion to be measured in the higher velocity groups. On wave-lengths much
in excess of 10 m. the transient echoes associated with meteors become
involved with various ionospheric effects and these longer wave-lengths
have been little used for work in meteor astronomy.
3595.68 E
IV
OBSERVATIONAL METHODS—III
RADIO-ECHO TECHNIQUES FOR THE MEASUREMENT OF
METEOR RADIANTS AND VELOCITIES
In the years between 1945 and 1950 there was a rapid development in
the application of the radio techniques discussed in Chapter III to
specific problems in meteor astronomy. In this book we are chiefly
concerned with the measurements of meteor radiants and velocities
and the present chapter will describe the more important radio techniques
which have been developed for these measurements. Various other radio
techniques, such as those for the measurement of meteor heights and
wind motions, lie outside the scope of this book.
1. The application of radio techniques to the measurement of
meteor radiants
Piercef first drew attention to the influence of the orientation of the
meteor trail with respect to the observing station, and subsequent experi¬
mental work by Hey and Stewart! and by Lovell, Ban well, and Clegg§
has shown that meteor trails do, in fact, show a critical aspect effect.
In most cases the radio echo is obtained only when the aerial beam is
directed at right angles to the trail. This property of meteor trails has
been used to determine the radiants of showers by observations of the
radio echoes. At least three methods have been described in the litera¬
ture, but the most widely used is that developed by Clegg (see (c)).
(a) The Method of Hey and Stewart
The first determination of meteor radiants by radio methods was made
by Hey and Stewart! who used three separate stations operating on
73 mc./s. situated as shown in Fig. 22. The direction of the aerials was
adjusted so that the beams intersected at a point about 100 km. in
height, equidistant from each station. Since a meteor trail will give a
radio echo only when it passes at right angles to the axis of the beam,
it is to be expected that as a radiant moves across the sky it will not
produce echoes simultaneously at the three stations, but in succession
as the meteor trails become oriented at right angles to the respective
f Pierce, J. A., Proc. Inst. Radio Engrs. 26 (1938), 892.
X Hey, J. S., and Stewart, G. S-, Nature, 158 (1946), 481; Proc. Phys. Soc. 59 (1947),
858.
§ Lovell, A. C. B., Banwell, C. J., and Clegg, J. A., Afon. Not. Roy. Astr. Soc. 107
(1947), 164.
01
IV § J RADIO. ECHO TECHNIQUES
aerial beams. The diurnal variations of the mean hourly rates obtained
by Hey and Stewart on the stations Bl, B2, B3 (Fig. 2 ) e w
July 26 -August 1 are shown in Fig. 23.
Static* B,
O *
Hrs GMT
Static* B,
(bearing &0‘)
n
msibS
Fio. 23. Diurnal variations of mean hourly rate of echoes on tho threo equip¬
ments of Fig. 22 from 1945 July 26-Aug. 1. Times at which the radiant R
(Fig. 24) is favourable are indicated by heavy-lines.
Ordinates =■ relative number. Abscissae - time G.M.T. O.A. - out of action.
The coverages of possible radiant points required to produce the peaks
in echo rate for B2 at 02h. 30m. and B3 at 04h. 30m. are shown in Fig. 24.
The centre of overlap R may be taken to be the radiant position and gives
a radiant point atf a 345°, 8—10°. The station Bl shows no marked
f The notation adopted for giving radiant coordinates in this book is a 345°, 8 — 10°,
indicating Right Ascension 345°, Declination —10°.
52
OBSERVATIONAL METHODS—III
IV. §1
peak. This is to be expected since a radiant in this position never presents
an aspect favourable to Bl. This radiant corresponds well with the
8 -Aquarid radiant, known to be prominent between these dates. The
accuracy of such a determination depends on the width of the aerial
beams. Hey and Stewart estimated that their errors in placing the
radiant due to this reason may be 10 °.
190 '
FlO. 24. Covorago of possible radiant positions for main
peaks in hourly rate of stations B2 and B3.
The method requires triplicate radio echo apparatus worked over long
base lines. Although important as the first radio determination of meteor
radiants it does not compete in simplicity or accuracy with a method
developed subsequently by Clegg (see below), and for these reasons it
has not since been used for radiant work.
( 6 ) The Methods of McKinley and Millman
(i) McKinley and Millmanf have described a method by which the
radiant of an isolated shower may be determined from a statistical
analysis of the radio echoes obtained on an apparatus using a fixed,
non-directional aerial system. The method is based on the possibility
of deriving the elevation of the radiant from the observed range distribu¬
tion of the echoes at given times. Assuming that all the meteors ionize
in a thin layer at a height of 100 km. above the ground and that the
meteors are entering the atmosphere at an angle <£ (i.e. the elevation of
the radiant) then the minimum slant range of the echoes observed will
be R = 100/cos <f>. The value of R is obtained for each hour when the
radiant is above the horizon from the plot of the number/range distribu¬
tion of the observed echoes. (Allowance for the sporadic meteor distribu¬
tion is made from data obtained when there is no active radiant.) The
t McKinley, D. W. R., and Millman, P. M., Proc. Inst. Radio Engrs. 37 (1949), 364.
IV §1 RADIO-ECHO TECHNIQUES 53
elevation of the radiant * is then calculated from the above formula, for
hourly intervals during the progress of the shower. The curve obtained
in this manner for the Geminid radiant on 1947 December 12-13 a shown
in Fig 25 The maximum elevation was 76° determined at Ottawa a
02h. 08m’ E.S.T. giving the radiant coordinates as «112° S+31°_
This is in good agreement with the best available data on the Geminid
Fio. 25. Variation of elevation of Geminid radiant during
tho night of 1947 Doc. 12-13 aa determined from tho rongo
distribution of the radio echoes by McKinloy and Millman.
radiant.t The probable error of the radio-echo determination is stated
to be between 2° and 3°.
This method can only be used if the echo rate is sufficient to yield a
satisfactory value of R at not more than hourly intervals. It therefore
requires the use of a comparatively long wave-length, high sensitivity
equipment (the wave-length used by McKinley and Millman was 9-2 m.),
and can only be used satisfactorily during an isolated active shower.
In the example quoted, Fig. 25 was derived from the range measurements
on 7,500 echoes. There are no published accounts of the use of this
method to determine the radiant coordinates of showers other than the
Geminid shower.
(ii) When fairly long radio wave-lengths of the order of 9 or 10 m.
are used, the radio echo can often be observed from the ionization over a
longer portion of the meteor path than in the neighbourhood of the
right-angle reflecting point. McKinley and Millman J used this property
to obtain simultaneous records of the meteor path from three triangularly
situated stations, with spacings of 36 to 57 km. If the meteor is moving
t See Chap. XV.
$ McKinley, D. W. R., and Millman, P. M., Canad. J. Rea. 27 (1949), 53.
OBSERVATIONAL METHODS—III
54
IV, §1
with constant velocity v, then the shape of the observed echo on a range¬
time display will be a hyperbola, defined by
R 2 = R?+v 2 (t—1 0 ) 2 , (la)
where R is the range at time t, and R 0 is the minimum range at time t 0
(that is R 0 is the perpendicular reflecting point). Clearly, if the hyper¬
bolae are sufficiently well defined on the three records then the R 0
points can be determined, and the path of the meteor in space can be
delineated. As will be discussed in § 2 the velocity is obtained from
the shape of the hyperbola. Thus, in principle, complete data are
available from which the orbit of a single meteor can be determined.
McKinley and Millman give one remarkable example of the three
simultaneous records of a meteor observed on 1948 August 4 which is
reproduced in Plate I, and from which it was possible to obtain the
data given in Table 9.
Table 9
Data on a Single Meteor obtained in the 3-Station Radio Measure¬
ments of McKinley and Millman
—-
Ottawa
Station (A)
Amprior
Station ( B)
CarUton Place
Station (C)
R 0 km.
117-8
108-6
122-1
t 0 8CC.
47-22
48-71
48-36
v km./sec.
34-7 ±0*8
35-3±0-6
35-1 ±0-6
Obsorved path length km..
270
175
180
Apparent geocentric velocity.
Apparent radiant: truo bearing
elevation .
True height above sea-level:
beginning of path
end of path
35 0±0-4 km./sec.
074°±2°
+ 2 °± 2 °
108 km.
104 km.
From these data it was possible to compute the orbit of the meteor.
Unfortunately the type of echo which gave the above records is rarely
observed. McKinley and Millman state that during 2,000 hours of
observation, they obtained only fifty echoes displaying an ionized path
well over 100 km. long, and of this number only a dozen while the three
stations were operating. In order to yield the type of record illustrated
in Plate I, the meteor must be travelling at a low angle to the horizontal
plane and must be of a mass sufficient to ensure that it will not be com¬
pletely vaporized during a period of several seconds. Although this
three station technique can yield the complete orbital data for a single
meteor it is unfortunately very restricted in its application. Apart from
65
IV § , RADIO-ECHO TECHNIQUES
the single case computed by McKinley and Millman there are no other
published records of its use.
Fio. 20. Tho chnnge in rango R* of meteors
detected at an elevation *, as the radiant
moves across the sky.
essentially on the specularly reflecting properties of meteor trails when
observed on wave-lengths in the neighbourhood of 4 m. If, on such a
wave-length, an infinitely narrow aerial beam is directed horizontally
in an easterly direction then radio echoes will only be observed from
meteors whose radiants lie in a great circle plane passing approximately
overhead and cutting the horizon in the north and south. Thus the time
of onset of echoes from an active radiant with such an idealized arrange¬
ment would give the right ascension of the radiant. By rotating the aerial
through an angle, and observing the difference in time of the onset of the
echoes in the two positions, the declination could also be found. Any
practicable aerial beam has a finite width in azimuth and elevation, and
thus echoes will be observed from a given radiant over a certain part of
its movement across the sky. During this movement of the radiant, the
range at which the echoes are observed will change as indicated in Fig.
26. If the meteors are assumed to originate at a constant height above
the earth’s surface, this layer will form a spherical cap above the
t Clegg, J. A., Phil. Mag. 39 (1948), 577; J. Bril. Astr. Ass. 58 (1948), 271.
So far the most extensively used method
:or radiants has been that devised by
ns can be determined with considerable
observations. The technique depends
(c) The Method of Clegg
(i) Theoretical considerations.
for the determination of met€
Cleggf whereby radiant positio
accuracy from single station
66
OBSERVATIONAL METHODS—III
IV, §1
observer at 0 due to earth curvature. Meteors detected due west at
zero elevation will have radiants lying on the great circle plane NZS;
those at elevation <f> will have radiants on the great circle plane NZ'S.
Hence, for an aerial directed towards the west, the ranges of the echoes
observed from the meteors of a given radiant will increase as the radiant
moves across the sky, but will decrease for an easterly directed aerial.
Fio. 27. Effective collecting aroa of aerial system.
The precise range-time relationships of the observed echoes depend on
the shape of the aerial beam. This was treated in detail by Clegg as
follows.
In an ideal meteor stream all meteors travel in parallel paths and due
to the effect of perspective appear to emanate from a point radiant. Fig.
27 represents such a stream viewed from a station at 0. The radiant lies
in the direction QR from the station, and the plane ABCD, which contains
0, is perpendicular to QR and cuts the celestial sphere in a great circle
of which the radiant is the pole. The path of all the meteors will be
parallel to QR and will cross ABCD normally, so that the reflecting
points will lie in this plane.
The majority of trails occur within a limited range of heights and this
further restricts the reflecting points to a strip of the plane of limited
depth. The echoes detected by the station will be from the portion of this
strip lying within the aerial beam. We thus define a collecting area
lying in the plane ABCD whose depth is limited by the depth of the
meteor zone, and whose lateral extent is determined by the width of the
aerial beam. It will be shown that with a knowledge of the radiation
pattern of the aerial it is possible to estimate the shape and size of this
collecting area for any position of the radiant, and conversely by
observation of the variations in range and echo rate to determine the
radiant position.
JV §1 RADIO-ECHO TECHNIQUES ° 7
The fundamental scattering formula (equation 6, Chap. Ill) may be
written for the present purpose in the form
z _ (!)
where
Z = amplitude of the echo measured as a signal to noise ratio,
G = effective power gain of the aerial system in the direction of the
reflecting point,
0 = azimuth of the reflecting point from the station,
= elevation of the reflecting point from the station,
a 0 = line density of electrons in the trail at the reflecting point,
R = range of the reflecting point from the station,
and k is a constant depending on the parameters of the apparatus. It
will be convenient to refer to a 0 as the effective electron density of the
trail.
Equation (1) may be written
O(M)
R«
q.
( 2 )
where Q = ( 3 )
If q remains constant, equation (2) defines a closed surface in space
on which the overall sensitivity of the apparatus is constant. There will
be a family of such surfaces corresponding to different values of q, those
of lower value completely enveloping those of higher value. These
surfaces will cut the great circle plane ABCD in a series of contours, as
shown in Fig. 27. For a single meteor stream, where the velocities of
the individual meteors are the same, it is assumed that all meteors of
the same mass will produce identical trails. Let the horizontal surface
STUV in Fig. 27 represent the height of maximum ionization for
meteors of a certain mass group. For such meteors the effective electron
density will be greatest when the trails cut the great circle plane in the
line Mj M 2 and will fall off with the increasing distance from this line.
Thus the amplitude of an echo will depend not only on the q contour on
which the reflecting point lies, but also on the distance of this point from
M, M 2 , and there will clearly be a closed curve such as xwyz in the plane
ABCD on which all trails of this class give echoes of the same amplitude.
A family of such curves can be drawn for different values of the signal
to noise ratio Z. If xwyz corresponds to a value of Z equal to unity, it
will represent the limit of visibility and the shaded area which it encloses
58
OBSERVATIONAL METHODS—III
IV, §1
will be the effective collecting area for meteors of this mass. For smaller
meteors the corresponding area will be less, and for the smallest detect¬
able mass group it will reduce to a point inside xwyz lying on the axis of
the beam OW. The collecting area for a larger mass group is shown as a
dotted line in the figure, completely enveloping xwyz.
For a given mass group the horizontal width xy of the collecting area
depends only on the conformation of the q contours on the great circle
plane, and for the largest meteors tends to a limit defined by the width
of the aerial beam. The depth wz increases indefinitely with the mass.
The method of radiant determination assumes that there are relatively
few meteors of great mass and that for the majority the depth of the
collecting area is small in comparison with its mean height above the
ground. In this case, if a surface such as STUV is drawn at the mean
height of maximum ionization for the shower, all the echoes will originate
at a point close to the line Mj M 2 , being most numerous close to the
point M 0 and occurring less frequently near to the edge of the beam.
To find the rate and ranges of the echoes for any position of the radiant
it is convenient to represent the aerial beam by a set of sensitivity con¬
tours on the surface STUV at the mean height of maximum ionization
as indicated in the map in Fig. 28. Let this surface be at a height h above
the ground. It can be shown that, allowing for earth curvature, the
range R and the elevation at any point on it are related by the equation
R 2 -f-2r 0 Rsin<£—2r 0 h-f h 2 = 0, (4)
where r 0 is the radius of the earth. The surfaces of constant sensitivity
will cut this horizontal surface in a series of contours defined by equations
(2) and (4). The map in Fig. 28 represents a polar projection of such a
surface at a height of 95 km., which may be taken as the mean height
of occurrence of a typical shower of medium velocity. The point 0 is
vertically above the station and, in order to illustrate a specific case, the
contours are drawn for one of the aerials at the Jodrell Bank Experi¬
mental Station.t This aerial has a half-amplitude beam-width of ±8°
horizontally and ±12° vertically. For the present purpose the beam is
maintained at a constant elevation of 12-5°, but can be directed at any
azimuth. The q values of the contours are marked, the contour q = 1
corresponding to the sensitivity at a point in this plane, situated vertically
above an aerial of unit gain. The shaded portions represent side lobes in
which the shape of the contours is not accurately known. Range circles
f Lovell, A. C. B., Ban well, C. J., and Clegg, J. A., Mon. Not. Roy. Aslr. Soc. 107
(1947), 164.
IV 5l BADIO-ECHO TECHNIQUES 6S
shown Riving distances from the station in kilometres. The dotted
“f 1 F jjG indicates where the spherical 95-km. surface meets the
horizon of the station. The radiant is in the azimuthal direction OR and
the curved line S.T.H shows where the great circle plane (ABCD, m
~ 27) cuts the 95-km. surface when the elevation of the radiant is
30°. As the radiant elevation increases, the point T moves farther from
Fio. 28. Map of sensitivity contours on a surface at a height of 95 km. for
a typical aerial in uso at the Jodrell Bank Experimental Station. Tho
radiant is in tho azimuthal direction OH.
0 and corresponding lines are shown for elevations of 60°, 75°, and 80°.
When the radiant elevation is 90° the line STH lies on the horizon circle
FHG, and for zero elevation it becomes the straight line S 0 OH, at right
angles to OR.
Let the radiant be at the azimuth indicated in the figure and at an
elevation 75°. The reflecting points of the trails will then lie close to
S 3 T 3 H, but visible echoes w'ill occur only within the limits of the aerial
beam. Consider the meteors whose mass is such that they give echoes of
noise amplitude when their point of maximum ionization lies on the
outermost contour, for which q = O il. The horizontal limits of the
collecting area for meteors of this class are defined by the points X a and Y 3
and, if the depth of the area (wz in Fig. 27) is not too great, these points
will determine the maximum and minimum ranges at which such meteors
can be detected. There will be a fairly well-defined upper mass limit above
60
OBSERVATIONAL METHODS—III
IV, §1
which relatively few meteors are to be found. If X 3 Y 3 defines the extent
of the collecting area for this limiting mass, it can be seen from the map
that the majority of echoes will occur between ranges of 530 km. and
890 km. At these ranges only the largest meteors will be seen, but at
points between X 3 and Y 3 meteors of smaller mass can be detected, and
the most probable range of the echoes will be that of MJ', where S 3 T 3 H
Fio. 29. Passago of radiant through central meridian with aorial
beam directed duo east.
touches the contour of highest value, and where the greatest number of
meteors will give visible echoes.
It is evident from this figure that for a radiant at the same azimuth,
but at elevation 60°, the ranges will be more scattered and the rate will
tend to be higher, while for an elevation of 80° the range will be confined
between narrower limits and the rate will be reduced.
As the celestial sphere rotates, the elevat ion and azimuth of the radiant,
and consequently the position of the line STH in Fig. 28, will change.
A typical case of a radiant sweeping through a low narrow beam is
illustrated in Fig. 29. Let the aerial be directed at azimuth 90° and the
radiant be about to cross the central meridian. Some time before transit
it is in the azimuthal direction ORj and the line STH lies completely
outside the beam so that no echoes will appear. As the azimuth ap¬
proaches 180°, STH will cross the limiting contour and the rate will
begin to rise, and at transit when the radiant is in the azimuthal direction
OR 2 the collecting area for large meteors will be defined by xy. After
transit the radiant passes through azimuths OR 3 and OR 4 . This will
cause a steady reduction in range and the echo rate will finally fall to
zero as STH passes out of the beam at W'. The passage of the radiant
through the beam is therefore characterized in this instance by a sudden
61
RADIO-ECHO TECHNIQUES
of echoes e. long r,„g» M—> by a slow fall in the mean
radiint at any right ascension and declination. In Fig. 30 a set
theoretical range-time curves is plotted for the aerial dcscnbed above at
azimuth 90°, assuming that the mean height of occurrence of the echoes
•Tkm. These curves are drawn for five different values of rachan
declination 8 (for an observer at the latitude of JodreU Bank, 53 N.)
andshow the variation of maximum, minimum, and most prohable rang
with time after transit, assuming that meteors can be detected out to
the contour q = O il. In each case the point B corresponds to the
time at which the line STH first crosses this contour, and, therelore, at
which echoes can first appear.
The curves show that there is a sudden rise in echo rate at a time close
to that of transit, and the rapid increase of the maximum and most
probable ranges to their highest value, followed by a steady fall. I‘or
radiants at low declination whose elevation at transit is small, the
initial rise in echo rate and range commences earlier and is less rapid
than for high declinations. Thus for declination -20°, ±0°, and +20
the rate has already become appreciable before transit and the maximum
ranges occur at transit as indicated in Figs. 30 (a), (6), and (c). For high
declinations the line STH docs not pass through contours of sufficiently
high value at the time of transit to ensure an appreciable rate, and the
range curves are similar to those shown in Figs. 30 (d) and (e). For an
aerial directed due west the variations occur in the opposite order and
the time scale in Fig. 30 is reversed.
Curves such as these can be constructed for any azimuth of the aerial
and it is always found that maximum ranges occur when the axis of the
beam is perpendicular to the horizontal direction of the radiant, provided
that the radiant elevation is not too great. If a different limiting contour
is chosen, or if the map is drawn for a different mean height of ionization,
the curves are of the same general form but the absolute values of the
ranges are altered.
By observing the well-known visual night-time streams for which the
radiant coordinates were known, Cleggf was able to show that the actual
shape of the range-time plots of the echoes agreed well with the theoretical
t Clegg. J. A., loc. cit.
Range (km)
-60 -50-40 -30 -20 40
10 20 30 40 SO 60 70 60 90 IOO 110 120 130 HO ISO 160 170160
Minutes after transit
Fio. 30. Variation of maximum, minimum, and most probable range with time
for observations taken on Jodrell Bank aerial directed at azimuth 90°. Curves
are computed from contour map of aerial assuming a moan height of occurrence
of 95 km. Maximum and minimum ranges apply to meteors which would be on
tho limit of visibility if their reflecting points lay on contours q = 0-11.
IVi§1 RADIO-ECHO TECHNIQUES
derivations discussed above. The method was then applied to the deter-
mination of unknown radiants in the following manner.
(ii) Application to determine radiant coordinates of unknown showers.--
Determination of right ascension. Theoretical range-time curves such
as those in Figs 30 (a), (6), and (c) show that for radiants at low elevation
maximum ranges occur when the azimuth of the radiant differs from that
of the aerial by 90°. The limiting elevation above which this no longer
applies depends on the mean height of occurrence and the intensity of
the ionization of the trails, but comparison of experimental results
with the theoretical curves showed that for the original apparatus usedf
it was invariably greater than 60°. Thus for a radiant whose elevation
never exceeds 60° (i.e. for which 8 = +23°) the right ascension can be
found by directing the aerial at azimuth 90°. Maximum ranges will then
occur at the time of transit. If the declination of the radiant is greater
than -j-23 0 , maximum ranges will generally occur after transit at some
time (t 0 -f-At 0 ), as indicated in Figs. 30 (d) and (e). The theoretical curves
show that At 0 will never exceed 15m., so that the consequent error in
right ascension will not be greater than 4°.
Determination of declination. It is possible to obtain some estimate of
the declination from the range-time distribution of the echoes after
transit, but for accurate determination it is necessary to make use of
the relationship between the declination and the rate of change of azi¬
muth of the radiant at the times close to transit. This relationship is
indicated in Fig. 31, in which the azimuth and elevation of the radiant
are plotted as functions of time. The curves are drawn for the approxi¬
mate latitude of Jodrell Bank (53° N.) and for a number of declinations
between 8 —40° and 8 +90°.
After observing the time t 0 of transit on azimuth 90°, the aerial is
turned to some arbitrarily chosen azimuth 90° -\-Q. If the radiant is at
sufficiently low elevation, maximum ranges will now occur when its
azimuth is 180°-f 0 at time t e . This gives the time t 0 — 1 0 required for
the azimuth to change from 180° to 18O°-f0 and immediately deter¬
mines the appropriate azimuth-time curve in Fig. 31 (a) and, hence, the
declination.
If the elevation of the radiant is greater than 60°, there will again be
an error, maximum ranges occurring on this new azimuth at some time
(tfl-J-Atfl). The apparent time required for the azimuth to change by 6
will then be (t#—t 0 H-At^—At 0 ). If, however, 6 does not exceed 20°,
the elevation of the radiant will not change appreciably during this
t Lovell, A. C. B., BanwelJ, C. J., and Clegg. J. A., loc. eit.
Elevation of radiant Azimuth of radiant (measured East of North)
Hours after transit
(b)
Fio. 31. (a) Radiant azimuth plotted as function of time after transit for
radiant declinations at 5° intervals between 8 —40° and 8 +90° and for latitude
63° N.
(6) Radiant elevation plotted as function of time after transit for radiant
declinations at 5° intervals between 8 —35° and 8 +90° and for latitude 53° N.
iv jl RADIO-ECHO TECHNIQUES B0
time and the errors At 0 and At, will be almost equal, so that the resultant
error in the declination will be negligible.
Method for radiants at higher declinations. If the observations described
above indicate that the declination is greater than +23°, the right
ascension can be found more accurately by choosing two aerial posi¬
tions 90 °—0 and 90°-f0 such that the elevation of the radiant when
at right angles to the beam is less than 60°. If maximum ranges occur
on these azimuths at time t_* and t 4 * respectively, the time of transit
will be and the radiant wdl have moved from azimuth
180 °—0 to azimuth 18O°-}-0 in time (t 4 $—1_$).
This method of radiant determination using a single movable aerial
was successfully employed to determine radiant coordinates during
much of the early radio-echo meteor work, particularly for the first
determinations of the radiants of the newly discovered summer day-time
meteor streams in 1947.| The technique suffered, however, from the
disadvantage that the aerial had to be moved in azimuth in order to
determine the declination and it was often impossible to obtain both
right ascension and declination measurements of a given radiant on the
same day. The technique was therefore modified in order to use two
fixed aerials at inclined directions with simultaneous photographic
recording of the echoes occurring in each aerial beam. The technique,
which has been described in detail by Aspinall, Clegg, and Hawkins}: is
outlined below.
(iii) The radiant survey apparatus at Jodrell Bank. In view of the
success of the above method for the determination of meteor radiants,
a special apparatus was constructed in order to determine both the right
ascension and declination during a single transit of an active radiant.
The apparatus also gives a continuous 24-hour record of meteoric
activity and has been in continuous use since 1949.
A schematic diagram of the apparatus is shown in Fig. 32. It operates
on a frequency of 72 mc./s., and comprises two independent beamed
aerials A x and A 2 , which are directed at low elevation, on azimuthal
bearings of 242° and 292° respectively^ These arrays are common to
the transmitter and receiver, and the pulses from the transmitter are
radiated simultaneously by both. The received signals are fed through
the transmitter-receiver switches S t , S 2 , into the pre-amplifying stages
t Clegg, J. A., Hughes, V. A., and Lovell, A. C. B., Mon. Not. Roy. Astr. Soc. 107
(1947), 369. (See also Chap. XVIII.)
J Aspinall, A., Clegg, J. A., and Hawkins, G. S., Phil. Mag. 42 (1951), 504.
§ The azimuthal directions being measured in degrees east of north.
F
3606.08
00
OBSERVATIONAL METHODS—III
IV, § 1
P„ P 2 , and after further amplification and detection are applied to the
grids of the intensity modulated display tubes D x and D 2 . The sequence
of operations is initiated from a master control unit by the unit T g ,
which provides pulses to trigger the transmitter, the multivibrator M,
and the common time base TB of the two display tubes. The square
waves from the multivibrator are used to suppress the preamplifying
stages P x and P 2 alternately, and are also applied to the grids of the
cathode-ray tubes D 1 and D 2 , so that the signals from each aerial are
displayed separately side by side, and are photographed on a film which
moves continuously in a direction perpendicular to that of the time bases.
The unit T g is capable of providing pulses with a number of different
recurrence frequencies, and the apparatus can be triggered in a variety
of ways. For normal observations the transmitter is usually operated
at a pulse recurrence frequency of 150 c./s. and the time base unit at a
frequency of 75 c./s. Under these circumstances the transmitter pulses
appear twice on each display, at the beginning of each time base and at
a range of 1,000 km. This serves as a useful check on the range calibra¬
tion, although subsidiary range markers can be supplied from the
triggering system at intervals of 200 or 250 km. along the time base.
One of the most serious difficulties encountered during the early experi¬
ments was that of differentiating between short duration echoes and
the random noise impulses which present a similar appearance on the
photographic record. This form of interference was considerably reduced
67
IV. §1
RADIO-ECHO TECHNIQUES
by inserting a discriminator unit, similar to that used by Davies and
EUyettf in the output of the receiver, but it has also been found advisable
to trigger the transmitter with a pair of pulses separated by approxi¬
mately 300 microsec., so that a true echo appears as a double. The
photographic records are similar to the illustrations of Fig. 21 and
Plate I. „ , . . .
Plate II shows the general arrangement of the two aerial systems,
which are situated at longitude 2° 18' W„ latitude 53° 14' N„ and are
placed symmetrically on either side of the building housing the trans¬
mitter and receiver. Each array consists of six Yagi aerials mounted
at horizontal distances of 1-2 A apart and at a height of 1-57 A above
the ground. They produce identical beams of elevation 8-5° and of half
amplitude width ±5° and have a power gain of 165 over a half-wave
dipole.
The minimum detectable signal at the receiver is 7 X 10" 14 w., and in
normal operation the peak power of the transmitter is 5 k\v., with a
pulse length of 8 microsec. Simultaneous visual and radio observations
have shown that under these conditions the echo rate produced by an
active shower, when the radiant is at 90° elongation to either of the
aerial beams, corresponds closely to the rate of occurrence of visual
meteors.
If the aerial characteristics are such that echoes can be detected down
to the horizon, R uittx is equal to the distance at which the meteor zone
cuts the horizon circle of the station, and for a typical shower of medium
velocity, for which the mean height of the zone can be taken as approxi¬
mately 95 km., R max = 1,100 km. Under these circumstances the time
of maximum range, T, is the time at which the azimuth of the radiant
differs from that of the beam by 90°. This would correspond to the
transit of the radiant for aerials directed to the east or west. For aerials
directed along azimuths 270°-f0, and 270°-f0 2 , the echoes reach a
maximum range at times T-f tj and T-f t 2 . The time difference t 2 — t x
is a function of the declination, 8, of the radiant, 0 V 0 2 , and the latitude
of the station. This function is plotted in Fig. 33 for the particular case
of the radiant survey apparatus at Jodrell Bank (6 l = —28°, d 2 = -f 22°
and lat. = 53° N.). From this curve the declination of the radiant may
be found, tj and t 2 may be determined separately by using the curve
labelled 1,100 km. in Fig. 34, and the time of transit then found from the
observed values of T-f tj and T-f t 2 .
It may be noted that t x is negative for radiants which transit south of
f Davies, J. G., and EUyett, C. D. (see § 2).
08
OBSERVATIONAL METHODS—III
IV. S 1
the zenith and that echoes appear first in aerial 1 and then in aerial 2.
For radiants which transit north of the zenith (decl. > 63°) this order is
reversed, and t,—tj becomes negative. If the declination is greater than
Fio. 33. Determination of declination from the times of maximum range
occurrence in the radiant survey apparatus.
tx or t, minutes of time
Fio. 34. Determination of right ascension from the times of max i m u m range
occurrence in the radiant survey apparatus.
76° the echo zone never enters the coverage of aerial 2, but remains for
many hours in the beam of aerial 1. A radiant position can still be deter¬
mined, however, by fitting theoretical range curves to the range/time
plots.
In practice, owing to the conditions governing the reflection of radio
waves from the surface of the earth, the aerial sensitivity falls off rapidly
in directions close to the horizontal, and echoes are never observed out
IV 5 , RADIO-ECHO TECHNIQUES 89
the curve of Fig. 33 and the determination of declination are not affected^
^naUy a smaU correction has to be applied if the mean height of the
^teors in a stream is not 95 km. This correction, which affects only the
of 1949 and 1950 which
are shown in Fig. 35, provide a typical example of the results <*tamed
with the apparatus. Times are shown as abscssae, and the ranges of
individual echoes are indicated by the lengths of the vertical lines. The
results obtained on each aerial between OOh. and 04h. U.T. on 1949
December 13 and 1950 December 13 are shown separately.
Table 10
Correction in Minutes of Time to be applied to Time of Transit for
Various Heights of Meteor Showers
Declination 5
Height
km.
-20°
-10°
0°
10°
20°
30°
40°
60°
60°
116
no
105
06
85
80
75
2
1
0
0
0
-1
-2
3
2
1
0
-1
-2
-3
4
3
1
0
-1
-3
-4
6
3
1
0
-1
-3
-5
6
4
1
0
-1
-4
-6
7
4
1
0
-1
-4
-7
8
6
2
0
-2
-6
-8
10
7
2
0
-2
-7
-10
12
8
3
0
-3
-8
-12
The plots in Fig. 35 show the variation in echo rate and range as the
echo zone sweeps through each beam in turn. The occurrence of echoes
at maximum range and the subsequent sharp fall in rate appear at about
Olh. 10m. U.T. on the first aerial, and at about 02h. 40m. U.T. on the
second aerial. The radiant positions obtained from these plots are as
follows:
Time of local transit
Radiant coordinates
1949 Doc. 13
02 h. 14 m. U.T.
a 111-5°
£ 32-6°
1950 Dec. 13
02 h. 18 m. U.T.
a 112-2°
5 32-5°
70
OBSERVATIONAL METHODS—III
IV, §1
Hours UT
Fio. 35. Examples of range-time plots obtained with the radiant survey
apparatus during the Geminid showers of 1949 and 1950 December.
The theoretical range-time plots for radiants in these positions are
shown as broken lines in Fig. 35. They provide a useful indication of the
diffuseness of the radiant, since, for a point radiant, all but sporadic
meteors should fall inside the envelopes.
RADIO-ECHO TECHNIQUES 7
"eU** rf th. pl.t. ob«i,d *• —' diJ "
J‘. h 0 .e„ E.™ —
F.o 36 Example* of range-time plots obtained with the radiant survey
t r ".t‘o8h"oTh 00m. and in aerial 2 at lOh.-lOh. 30m. In each
caso it is followed by the (-Pereeid radiant.
exceptional case of a major stream with a radiant lying within 20° of
the celestial pole the position must be determined by the curve-fitting
method, and the accuracy is reduced. For weaker streams the accuracy
falls off markedly with decreasing echo rate.
The apparatus can only resolve two radiants which are active simul¬
taneously if their range-time plots on at least one of the aerials are separa¬
ted by approximately 30 minutes. This time separation depends on the
relative positions of the two radiants, and may be expressed in terms of
their angular separation and relative position angle 6 0 . Fig. 37 represents
a small portion of the celestial sphere viewed internally, with two radiants
at R„R S . If ABC is the meridian bisecting the great circle arc R 2 R a
at B, then 0 O is defined as the angle ABR 2 . Fig. 38 shows the angular
72
OBSERVATIONAL METHODS—III
IV, §1
separation required for resolution on each of the two aerials, plotted as
a function of 0 O for different values of the declination of R v It is evident
that any pair of radiants whose angular separation is greater than 20°
Fio. 37. Relative position angle 6 0
of radiant* R, and R,.
Fio. 38. Angular separation of two radiant* required for resolution
on each of the aerials of the radiant survey apparatus.
can be resolved by at least one of the two aerials, while for more favour¬
able cases the degree of resolution is considerably higher than this.
All the radio-echo radiant determinations since 1949 quoted in
Chapters XIII-XVIII have been made with this apparatus, which
RANGE IN
• 'vV
A - OTTAWA
£.51
280
260
240
220
* 180
160
140
120
B-ARNPRIOR C-CARLETON PLACE
Mrtror pin»iotfraping nt ilini* am l!»4« Ainriu-l I. (Kr|inNlucinl »»y kitiil
|N*rmi>«ion of l)r. D. \V. K. MiKink'V dm I Dr. I*. M. Milliium.)
Tin* |»liolo*rnipl»«« >lio\v:
Amvl.. i.v p. ri'olii -i..i| • ii ITli •■'•in. 13 XU from whirli tin* niuiii ilnld«uv
hi i Aimm Iio III I Til. .Vim. .1%.. • iHliirm.’ I**r 27 i.mh. i Mi.m.i m-m.l. Tln-.i-lin lir-i .it
n true ln’i^hl • I«• l km. »nh iNurititf 197 nimI khmiimI «li*i«•••••* 120 km. limn Ottawa. Afli*r
|*, mt. tin* In-iirlii *>l lit.-. i lin «m% '-‘I km. ami tin- apium-nt .lull nf tin- «*'lm uu*nl.nui 2nkm.
mi a soulh-i-ii'l ilirii ln.il.
mu \ i>il.li- mi ill.- Oiinw.i |.lM»l*^:ra|.li niily an-un i-rhn hi I Tli. V»ni. .Vk raiiL 1 '' 270 km., iluriit inn
mu- ii-rmul. mnl an ,.i I Tli. V»m. V*-.. r.niir*- 22Mo 2Hi km. A- I In-*- n-luu-s • 1 1 <I iml ii|>|i* ar
a( ill.* nllii-r -ia!mu- n nu> tint |Mr.*iMt- in t nnmrulnt <- Ii*-»irl»i. iihI |Mi>ilinn-».
I* LATH
Tin* IH'rill I svsli'iii of till- i-.iiliant survi-y ii|i|>nrut u* at .lotln'll Hunk.
In tin* liirln iMii-kuronnil fan lif «irn a rtn.ft. ilimni'tfr stcfralili*
DifTruction pat torn from a meteor trail obtained with pulsoil rndio-ceho equipment. (Cf. 1 Iteoret ie.d slmpe
in Fig. 3!».)
Tlie velocity of the meteor ninauml from the zone spaeinc was .»l*7 J_2%i km./see.
IViJ , RADIO-ECHO TECHNIQUES
has also yielded the data on sporadic meteor radiants discussed in
Chapter VI.
2. The application of radio techniques to the measurement of
meteor velocities
Two distinct radio-echo methods of measuring meteor velocities have
been developed. The first records the range of the meteor against time
and can only be used satisfactorily with densely ionizing meteors under
conditions when a radio echo is returned from the iomzation near the
head of the meteor. The second, more generally applicable method,
records the amplitude variations with time as the meteor crosses the
foot of the perpendicular from the observing station to the trail. This
involves only a very short time interval near the instant when the
meteor is at the perpendicular point and, in principle, can be employed
for any meteor which gives a strong enough echo to be recorded. With
conventional equipment of the type already discussed the number of
meteors susceptible to velocity measurements by the two methods is
about 1,000 to 1 in favour of the amplitude-time method. The range-time
method is important, however, in the case of densely ionizing meteors
which can be observed over a considerable length of their path since
measurements of deceleration become possible, and triangulation enables
the orbit of a single meteor to be determined as described in § 1 (6).
(a) Range-time Methods
In this method a pulsed transmitter is used and the received echo is
displayed on an intensity-modulated range-time display. If the radio
wave-length is long enough, and the ionization is sufficiently dense, then
an echo may be recorded from parts of the ionized trail which are at a
distance from the perpendicular reflecting point. In this case, as dis¬
cussed in § 1 (6), the recorded echo will be in the shape of a hyperbola as
given by equation (la). An extremely good example of this type of
echo obtained by McKinley and Millman| is shown in Plate I. In this,
both the approach and the regression of the meteor can be observed.
The production of a radio echo from the neighbourhood of the
minimum range point (R 0 ) in terms of diffraction from a line source is
now well understood (cf. Chap. Ill and later in this chapter). It is
unlikely, however, that echoes of the type illustrated in Plate I can be
explained in this way (that is apart from the minimum range point
reflection). The intensity of the diffracted echo will vary inversely as
the distance from R 0 and should therefore be very weak for remote
f McKinley, D. W. R., and Millman, P. M., Canad. J. Res. 27 (1949), 53.
74 OBSERVATIONAL METHODS—III IV, § 2
points and increase steadily near R 0 . The echoes do not show this
behaviour, however, and have other features which make such an
explanation of the reflection untenable. It seems certain that some
mechanism exists in these densely ionizing meteors which is capable of
giving a reflection from the ionization near the head of the meteor. No
satisfactory explanation of the mechanism exists. It must differ from
the conventional meteoric ionization processes discussed in Chapter III
because if the idea of reflection from a line source is abandoned, then a
considerable area of ionized matter above the critical density must exist
in the region of the head. One hypothesis advanced by McKinley and
Millmanf is that ultra-violet light from the head of the meteor instantly
ionizes the air at a considerable distance from the meteor. The echoing
area of such a cloud would be relatively independent of the angle of
incidence of the radio waves.
The geometrical analysis of the reflection of radio waves from such
a ‘moving-ball’ type of target was considered by Manning.^ who worked
out the interference effects and the frequency of the Doppler whistle
which would be observed when c.w. radio waves reflected from such a
target interacted with the direct ground wave. Manning applied his
analysis to all types of meteor echoes, the majority of which we now
believe to arise from scattering near the R 0 point only and to be explained
by the diffraction theory (§ 2 (6)). In actual fact Manning’s analysis
is now believed to apply only to the rare cases of the echoes discussed
in this section. In fact, in the case of such densely ionizing meteors,
McKinley§ has given evidence of the simultaneous observation of both
the interference and diffraction effects near the R 0 point.
The first range-time velocity measurements were made by Hey,
Parsons, and Stewart|| during the great Giacobinid meteor shower of
1946 October. Although their apparatus worked on the comparatively
short wave-length of 5 m. the shower contained meteors of sufficient
magnitude to yield twenty-two faint fast-moving echoes prior to the
R 0 echo from which they were able to measure the velocity ft by applica¬
tion of equation (la). The experiment is of great historic interest in
representing the first successful measurements of meteor velocities by
radio methods. The range-time methods were later developed further
f McKinley, D. W. R., and Millman, P. M., Proc. Inst. Radio Engrs. 37 (1949), 364;
McKinley, D. W. R., J. Appl. Phys. 22 (1951), 202.
X Manning, L. A., J. Appl. Phys. 19 (1948), 689.
§ McKinley, D. W. R., loc. cit.
|| Hey, J. S., Parsons, S. J., and Stewart, G. S., Mon. Not. Roy. Astr. Soc. 107 (1947),
176.
ft See Chap. XVI.
IV, §2
RADIO-ECHO TECHNIQUES
76
McKinley and Millmanf using longer radio wave-lengths in the region
n o m and have been applied by them to the measurement of velocities
° d of decelerations-! On these longer wave-lengths the echoes of hyper-
hnlic shape appear more frequently and extend over a considerably
eater path length than those observed by Hey, Parsons, and Stewart.
Four methods of measuring the velocity from a range-time echo such as
that illustrated in Plate I have been described by McKinley and Millman.§
(i) Curve-fitting method. Hyperbolic curves may be fitted directly to
an enlargement of the echo and the best fit determined by trial and error.
Owing to the various small distortions which are present in the record
it is preferable to transfer the curve point by point to Cartesian co¬
ordinate paper, introducing any necessary corrections to each R and t
point. A series of hyperbolic curves is then constructed with the
observed values of R 0 and t 0 and various values of v, from which the
probable upper and lower limits of v can be assigned.
1 (ii) forge x dR/dt method. Plate I is a good example of a range-time
record which includes the (R„,t 0 ) point, but in many cases only segments
of the hyperbola are recorded, excluding this minimum range point. In
this case the velocity can be derived from the curvature of the segment.
Differentiating equation (1 a) (p. 54),
R^ = v*t-v%.
at
(5)
The slope of R is therefore v 2 . This curve can be constructed from
the measured value of dR/dt along the segment.
(iii) Three-point method. In (1 a) v 2 may be evaluated by substituting
three values of R and t from widely different parts of the observed curve,
v is then given by
(t 2 —t 1 )(t 3 —t 2 )(t 3 —1 4 )
(iv) Parabolic regression method. The velocity may also be computed
by using the curvilinear regression method of least squares.|| In (la)
if R 2 is replaced by p then the observed values give a parabolic relation
between p and t. The equations are then solved in the usual manner.
f Millman, P. M., and McKinley, D. W. R., J. Roy. Astr. Soc. Can. 42 (1948), 121;
McKinley, D. W. R., and Millman, P. M., Canad. J. Rts. 27 (1949), 53; McKinley,
D. W. R., J. Appl. Phys. 22 (1951), 202.
x McKinley, D. W. R., loc. cit.
§ McKinley, D. W. R., and Millman, P. M., loc. cit.
|| See, for example, Hoel, P. G., Introduction to Mathematical Statistics, Wiley, N.Y.,
1947.
76
0B8EEVATI0NAL METHODS—III
IV. | 2
McKinley and Millman used all four methods in treating the example
shown in Plate I, and found that the results agreed within the limits of
error. The greatest source of error in the range-time measurements lies
in the ambiguity as to the real outline of the echo hyperbola. In general
it would appear to be difficult to reduce the final errors in the velocity
below 1 or 2 per cent.
After the pioneer measurements of Hey, Parsons, and Stewart on
the Giacobinid shower the range-time technique for velocity measure¬
ment has been almost exclusively developed by McKinley and Millman.
Even on the long wave-lengths used by them the number of echoes
suitable for analysis of this type is rather small and the greatest value
of the technique is for special purposes such as measurement of decelera¬
tions, or the orbits of single meteors from three-station triangulation.
The major part of the work on the measurement of meteor velocities has
been carried out using one of the amplitude-time methods described
below.
(6) Amplitude-time Methods
The diffraction theory of the scattering of radio waves from the
neighbourhood of the R 0 point on a meteor trail was first given by Lovell
and Clegg.t The idea that the change in intensity of the echo as the
meteor passed the R 0 point might be used to measure the velocity was
due to HerlofsonJ and the first successful application of the idea to
measure velocities was made by Davies and Ellyett§ using the pulse
method. Subsequently, continuous-wave techniques were applied to
the problem by Manning, Villard, and Peterson,|| and by McKinley.tt
The shape of the diffraction pattern to be expected, and the strict
analogy with the optical case of diffraction, was demonstrated by
Davies and Ellyett.§ A later, more comprehensive, treatment by
McKinley ft included various aspects of the continuous-wave case, and
will be followed here.
Equation (1 a) will be written in the form
R* = RJ-f v J (t-t 0 )> = R§+s a , (7)
where s is the distance along the meteor path measured from the mini¬
mum range point (R 0 , t 0 ). The wave scattered from an element of meteor
f Lovell. A. C. B.. and Clegg. J. A., Proc. Phya. Soc. 60 (1948), 491. (See also Chap. II.)
t Herlofson, N.. Rep. Phya. Soc. Progr. Phya. 11 (1948). 449. .
§ Davies. J. G.. and Ellyett, C. D., Phil. Mag. 40 (1949), 614; EUyetfc, C. D., and
Davies, J. G., Nature, 161 (1948), 696.
|| Manning, L. A., Villard, O. G-, and Peterson, A. M., J. Appl. Phya. 20 (1949), 476.
If McKinley, D. W. R., Aatrophya. J. 113 (1961), 225.
RADIO-ECHO TECHNIQUES
77
IV, §2
path ds will be
&A
= g(R,oo)ain|wt
47tR
A I
( 8 )
„ „d A rf. » th. *»- £
: —- -
eignal reflected from the section 8,8 will be given by
'
| r = g(R,o 0 ) J
sin loit
(9)
The integral can be evaluated by using the approximation near the
t 0 point R ~ R 0 +(s 2 / 2R o)-
Writing
<I> = cot
nx l
and
2n8 2
R 0 A'
^ _e,J do)
X,
where E r has the dimensions of field strength and is constant for a given
meteor. Equation (10) may be expanded as
A r = E r (Csin<I>-Scos<I>), ( u )
where
ttx* ,
cos—dx
(C and S are the conventional Fresnel integrals of optical theory.) The
frequency of the variations in C and S are small compared with to. It
can he shown that the contribution from the lower limit x, is generally
negligible, and hence the lower limit can be taken as —co.
f Lovell, A. C. B., and Clegg, J. A., Proc. Phys. Soc. 60 (1948), 491.
(See also Chap. II.)
78 OBSERVATIONAL METHODS—III IV, § 2
The intensity of the reflected wave is given by (11) as
I r = E?(C*+S*), (12)
an expression identical with that for the case of diffraction of light at a
straight edge. It represents a steadily increasing intensity up to the t 0
point after which the intensity oscillates about a final mean value as
shown in Fig. 39.
(i) Pulse techniques for observation of the diffraction pattern. The
demonstration that the reflected wave followed the amplitude-time
pattern of Fig. 39 was first made by Ellyett and Davies.f Special
Fio. 39. The theoretical amplitude-time pattern to bo expected as the meteor
crosses tho foot of tho perpendicular P from the observing station to the trail.
technical developments were necessary in order to observe the diffrac¬
tion pattern. On the wave-lengths used (say A = 4 m.) the zone lengths
are of the order of 0-5 km. for a meteor at a range of 100 km.; thus for
meteor velocities of the order of 40 km./sec. the time intervals between
successive maxima and minima are milliseconds only. In order to
observe the amplitude variations of the scattered echo within this
period the transmitter was pulsed at a recurrence frequency of about
600 per second giving a separation between pulses of about 1-7 millisec.
The echo was photographed on a single-stroke time base of speed
sufficient to resolve the individual pulses, giving an amplitude-time
record of the type illustrated in Plate III in which the zone pattern is
t Ellyett, C. D., and Davies, J. G., loc. cit.
79
IV §2 RADIO-ECHO techniques
and other details of the apparatus have been demited by
Ellyett. f The range of the eeho was measured s.multaneously by
photographing a separate conventional range-tune disptay.
The proof that the observed echo patterns similar to Plate III were
actually the diffraction effects given by equation (12) wasmade by
measuring the meteors in a shower of known homogeneous vebmty
such as the Geminids. Then if v 0 is the apparent geocentric velocity
the meteors in the homogeneous group, p the number of
between specific zone maxima or minima, t the interval between specific
zone maxima or minima, and f 0 the pulse recurrence frequency, it
evident that V(RA) (13)
V 0 = o*0 “ * '
Thus, for a series of meteors with identical velocities,
= const., O 4 )
P
and, if such meteors are observed at various ranges, widely varying
values should be obtained for (x/p) mcan (which is a measure of the time
required to traverse a Fresnel zone); but the values of (x/p) mcfin ' K
should remain constant. The validity of this result was first established
by Davies and Ellyett during the Geminid meteor shower of 1947
December.
This pulse technique has since been extensively used at Jodrell Bank
for the measurement of the velocities of shower and sporadic meteors,
and many of the results are contained in later chapters.
(ii) Continuous-wave techniques for the observation of the diffraction
pattern. If the transmitter radiates continuous waves instead of pulses
then the fundamental diffraction theory given above will still apply but
the recorded envelope will be continuous. If, in addition, the signal
scattered from the meteor trail is allowed to beat with a direct ground
wave from the transmitter then the diffraction pattern can be observed
f Davies, J. G., and Ellyett, C. D. t loc. cit.
80
OBSERVATIONAL METHODS—III
IV, §2
both before and after the minimum range point.f The extension of the
diffraction theory given above to the case of continuous-wave signals
with ground wave injection has been given by McKinley4
Suppose the receiver picks up a small fraction of the transmitted
power directly of amplitude A d given by
A d = E d sin (cot—
where D is the distance between transmitter and receiver. This will be
added to the amplitude A r from the meteor, given by equation (11),
producing the combined intensity:
I r+d = EJ(C 2 -f S 2 )-f EJ-f 2E r E d (Ccos0 — Ssin^r) (16)
= (E r C -f E d cos ^)*-f (E r S — E d sin ip) 2 , (17)
where tp = ^^ 0 —P? lB the phase difference between the direct and
A
reflected paths at time t 0 .
The signal actually obtained at the receiver output will depend on the
type of detector. A square-law detector will reproduce the intensities
given by (12), (16), and (17) directly. A linear detector will follow the
square root of the intensity. The theoretical wave forms can be calcu¬
lated for various p values and ratios of A d to A r . They are given in
Fig. 40 for equal intensities of direct and reflected waves (EJ = 2E 2 )
and in Fig. 41 for 2EJ < EJ.
If the region (—1 > x > 1) around the t 0 point is excluded, Cauchy’s
approximations for the Fresnel integrals give (assuming Xj to be —co):
On the approach side of t 0 , (—s)
C = -sin?£,
ttX 2
— COS
TTX
On the receding side of t 0 , (+s)
C=l +
1
sin
ttX'
TTX
S = 1—-coa^.
TTX 2
f The term ‘Doppler whistle’ is often applied to the echoes obtained by the con¬
tinuous-wave method because if the output of the receiver is connected to a loudspeaker,
a whistle of varying pitch is heard (see, for example, Chap. II). The original idea that
these whistles were a true Doppler effect arising from the wave reflected from the head
of the meteor beating with the ground wave has been abandoned, since it can only occur
in relatively infrequent cases of meteors of exceptional brightness. It is now recognized
that the whistles arise from the amplitude and frequency changes in the diffraction
patterns discussed in this chapter. Actually there is little difference in the calculated
‘whistle’ frequencies (except near the t, point) given by the interference and diffraction
theories.
$ McKinley, D. W. R., Astrophys. J., loc. cit.
81
RADIO-ECHO TECHNIQUES
Fxo. 40. Theoretical amplitudo-timo records. 2E? * E^.
Fio. 41. Theoretical amplitude-timo records. 2EJ < E^.
Equations (18) and (19) are together equivalent to (12). Thus for the
case of the reflected and ground wave
w-»=+4 < 2 °>
which shows that the diffraction effect is also now observed on the
8695.00
Q
82
OBSERVATIONAL METHODS—III
IV, §2
approach side, whereas without the ground wave it is only observed on
the receding side.
After t 0
W+8) = ES+2E?-*
2E
E?
7 T 2 X 2
2V2E
r E d sin^-^
+
+
J [E5+2EJ-2V2E r E d 8in^-^] J X
—Ed
+E d cos^
X sin
tan
-,/ E r -E d sin^ U
U r+ E d C 08 ^}- (21)
If t is the time relative to the t 0 point then the instantaneous frequency
of the oscillatory terms in (19), (20), (21) can be shown to be
'-S*- (22)
Thus the slope of f against t is proportional to the square of the meteor
velocity which can be calculated if R 0 is also measured. As mentioned
above, this measurement requires a separate pulsed equipment.
Equation ( 22 ) is the same relationship obtained by Manningf working
on the basis of a ‘moving-ball’ type of target giving an interference
effect. The agreement is fortuitous since the interference theory does
not predict the other characteristics of the observed echoes, and, as
discussed on p. 74, it is now believed to apply only to the infrequent
cases of very large densely ionizing meteors.
The c.w. methods for velocity measurement have been used at Stan¬
ford by Manning, Villard, and PetersonJ and most extensively by
McKinley§ at Ottawa, whose technique will serve as an illustration of
the experimental arrangements. The continuous-wave transmitter had
a c.w. output of 1*6 kw. on 30 02 mc./sec. and fed into a half-wave dipole
mounted a quarter wave-length above ground. A similar dipole was
used as receiver, the axis of the two being collinear in order to reduce
pick up of the direct ground wave. The receiving site was 7-5 km. from
the transmitter. Two types of recording were used. In the so-called
‘slow Doppler’ method which was generally used, the receiver output
was applied to a cathode-ray tube as vertical amplitude modulation of
a horizontally moving trace which was photographed by a film moving
vertically at 4 inches per minute. This speed was the same as that of the
film recording the intensity-modulated range-time trace of the pulsed
f Manning, L. A., J. Appl. Phys. 19 (1948), 689.
X Manning, L. A., Villard, O. G., and Peterson, A. M., ibid. 20 (1949), 476.
§ McKinley, D. W. R., Astrophys. J. 113 (1951), 225.
Fio. 42. Two meteor echoes. Velocities: (a) 28 km./sec.; (6) 47 km./sec. Top:
range-time record (using pulsed equipment). Centre: c.w. amplitude-time
record, ‘slow Doppler’ method. Bottom: c.w. amplitude-time record, 'fast
Doppler’ method.
Fio. 43. Some examples of observed amplitude-time moteor echo records
on a c.w. equipment recorded with the ‘fast Doppler’ system.
RADIO-ECHO TECHNIQUES
85
the^fmplitude modulation is applied horizontally to a stationarjH^hode^
TZ spot and the film ia drawn past at 4 inches per second The
equivalent Doppler’ records of the meteors in Fig. 42 (a) and (6) are
shown in the lower reproduction. Fig. 43 shows other examples of the
'fast Doppler’ records, some of which show striking sumlant.es to the
ts -rrar—^
interval At between the m-th and n-th cycles and calculated the velocity
fr ° m v = V(R 0 A)(^). (23)
The probable error of the measurements, including contributions from
all sources, was estimated as 6 per cent.
Many of the velocity measurements made by these c.w. techniques are
referred to in later chapters on the sporadic and shower meteors. In
comparing the c.w. and pulse techniques of amplitude-time velocity
measurements, it is evident that the c.w. method has certain advantages
in that the diffraction pattern can be observed both before and after the
t point, the zones are often more clearly defined and generally more are
available for measurement than in the pulse case. There is, however,
the great disadvantage that three separate aerial systems are needed-
one at the transmitter, one at the receiver, which has to be separated by
some kilometres for satisfactory ground-wave injection, and one for
the separate pulse apparatus required for range measurement. Little
difficulty arises as long as simple dipole systems are used, but when
high-gain aerials are used for the investigation of faint meteors the c.w.
system is scarcely a practicable alternative to the pulse arrangement
which requires only a single aerial.
| McKinley, D. W. R., Asirophya. J., loc. cit.
V
THE FUNDAMENTAL EQUATIONS OF
METEORIC MOTION
It has already been mentioned in Chapter II that on the night of the great
shower of Leonid meteors, 1833 November 12-13, many observers
recognized that the meteors appeared to be diverging from a point in the
sky. Very soon Olmsted and Twining suggested that the shower was
caused by a cloud of particles through which the earth passed, and the
idea of a periodic phenomenon arose. The quantitative developments of
these ideas, which emphasized the importance of determining the spatial
orbits of the meteoric particles, were made by Schiaparelli, H. A. Newton,
and others in the second half of the nineteenth century.
Much of the observational effort described in this book has been
devoted to the measurement of two quantities. Firstly the radiant,
that is the point in space from which a meteor appears to originate, or
in the case of a shower the point or area of space from which the meteors
appear to diverge. Secondly the velocity with which the meteor—or, in
the case of a shower, the meteors—travel in the earth’s atmosphere.
If these two quantities are known then it is possible to calculate the
spatial orbit of the meteor. The computation is based on well-known
principles of celestial mechanics and has been described by Olivier,f
Porter ,% and many others. The method will be summarized in this
chapter in order to define the terms which occur later in the text.
1. The elements of the orbit
In Fig. 44 the sun S is at one focus of the ellipse PBA, with semi-major
axis a and semi-minor axis b. If e is the eccentricity then the perihelion
distance q = a(l—e) and the aphelion distance q' = SA = a(l-f-e). PA
is the line of apsides. The semi-latus rectum p = a(l—e 2 ). In the case
of a hyperbola (e > 1), a will be negative. In the case of a parabola (e = 1)
the shape of the orbit is defined completely by q, with p = 2q.
In Fig. 45, i is the inclination of the plane of the orbit to the plane of
the ecliptic. If i > 90° the motion of the meteor is retrograde (that is
opposite to the direction of motion of the planets). The ascending node
SI is the point at which the meteor passes from the south to north side
t Olivier, C. P., Meteors, 1925.
X Porter, J. G., Cornels and Meteor Streams, Chapman & Hall, 1962.
87
v , , EQUATIONS OF METEORIC MOTION ^
“^ f
perihelion «. The longitude of perihehon * - «+
B
Hence the size of the meteoric orbit is defined by a .to shape by e
the orientation of its plane in space by i and SI, and the duecUon o
the major axis in that plane by «, The position in the orbit has to be
defined by a sixth element^-the time of perihelion passage T g
by angles known as ‘anomalies’. In Fig. 46. if the meteor is at M. then
the angle between the radius vector r and the line of apsides is the true
anomaly v. The eccentric anomaly is the angle E. the construction being
evident from Fig. 46. The mean anomaly M = n(t-T), where n is the
mean daily motion in degrees and t the date.
EQUATIONS OF METEORIC MOTION
V. SI
88
2. The velocity of the meteor in its orbit
If, in Fig. 46, the sun S is taken as the origin of X and Y axes in the
plane of the orbit then .
x = r cos v 1
y = TBinv J (*)
The velocity V of the meteor in the orbit is given by
\dt) Vdty
\dt) + \dt/ •
This can be expressed in terms of r and a as follows:
The accelerations along X and Y are given by
d 2 x/dt 2 = — Acosv == — Ax/r \
d^/dt 2 = —Asini/ = — Ay/r J
Thus x d*y/dt 2 — y d 2 x/dt 2 = 0,
the integral of which is
x dy/dt — y dx/dt = h,
where h is the constant of integration.
Transferring to polar coordinates,
( 2 )
(3)
(4)
(5)
( 6 )
(7)
y 52 EQUATIONS OF METEORIC MOTION
89
Further, from equations (4),
xd 2 x yd*y- A
r dt 2 1 r dt 2
(8)
which becomes
d*r r (dv\*__ A
dt 2 \dt/
(9)
in polar coordinates.
Since
r P
1 -fecosv’
(10)
then, using (7),
dr eh sin v
dt p
(11)
Equations (7) and (11)
can now be substituted in (3) giving
■ry, h 2 , e 2 h 2 em 2 v
r 2 + p 2
(12)
= ^!(l-|-e 2 -l-2ecos»/)
P
(13)
(14)
Further, if M is the mass of the sun, the acceleration of a meteor of mass
m relative to the sun will be Y(Af ± — > , or the acceleration at unit
distance (t = Y(M+m). Writing Y = k 2 , and expressing masses in
terms of the sun’s mass as unity,
(i = y( 1 + ™) = k 2 (l + m).
Also, since m is negligible, |A = Y = k 2 .
Manipulation of equations (7), (9), and (11) also gives
But the acceleration is also k 2 /r 2 : thus k 2 = A 2 /p, and (14) becomes
V 2 = k 2 (?-i), (15)
which is the fundamental expression for the velocity of a meteor in its
orbit around the sun.
If the meteor is moving in a parabola, a = co and (15) becomes
vs = »
(16)
EQUATIONS OF METEORIC MOTION
90
V. §2
If the meteor is moving in a hyperbola then a is negative and (15) becomes
Vl = k *(?+i)- < 17 >
It will be seen later that the parabolic limiting velocity given by (16) is
of great importance, and the question as to whether the velocity of
sporadic meteors lies above or below this value has led to a deep contro¬
versy.
Fio. 47. The apparent radiant of a meteor.
3. The velocity of the meteor in the earth’s atmosphere
The velocity V given by (15) is the heliocentric velocity of the meteor,
or its velocity in the orbit before coming under the influence of the
earth. In Fig. 47 it is represented in magnitude and direction by TE.
The apparent velocity V of the meteor will be compounded of the
heliocentric velocity V and the earth’s velocity V E .t In Fig. 47 it is
represented by RE. The actual velocity measured by an observer on
the earth will be greater than V because the attraction of the earth on
the meteor forces it to move in a hyperbolic orbit about the earth’s
centre. This observed velocity v is known as the geocentric velocity
of the meteor. If is the acceleration at unit distance from the earth,
then by (17) the geocentric velocity will be given by
<i! >
where r 0 and a e refer to the hyperbola about the earth’s centre. The
apparent velocity V outside the range of the earth’s attraction must
f V B is not, of course, constant. If ita mean value is taken as unity then in (16)
k a is unity and V| = 2/R—1, where R is the aim’s radius vector, obtainable from
standard tables for each day of the year.
v §3 EQUATIONS OF METEORIC MOTION
also be given by (18) when r = co so that
V« = ^.
a.
Hence
and
r 2 —,
V 2 + 2^?
V 2 (2a 0 +r e ) = v*r„.
01
(19)
( 20 )
( 21 )
, = Vm where m„ is the mass of the earth. If this is taken as
3*03 X 10"* of the sun's mass, and the distance as that from the centre
of the earth to the meteor when it enters the atmosphere (say 6,450 km.
= 4 - 31 X10" 5 a.u.), then
Hence
2^ _ 2k 2 m, _ 124 . 9
r o
,2 = v 2 +124-9.
(221
4. Corrections to the observed radiant
(a) Zenith Attraction
The gravitational attraction of the earth on the meteor not only
increases the velocity from V to v as given by (22), but also changes the
direction in which the meteor is moving. In Fig. 48 the meteor M at a
distance from the earth may be considered to be moving along the
straight line MC, but on approaching the earth it will be forced into tho
hyperbola MPM', with centre C and foci at S, the earth’s centre, and at
S'. Then SC = CS' = a 0 and PS' = r 8 +2a„, where r 0 is the radius of
the earth. If TP is the tangent to the hyperbola at P then an observer
at P measures the zenith distance of the radiant as z = TPR. In fact,
the correct zenith distance is z = fQR, where TQ is the asymptote
to the hyperbola (meeting the major axis at C, so that sec £ = e). Thus
the measured radiant is always displaced towards the oberver's zenith,
and the effect is known as zenith attraction. The value may be deduced
as follows:
The projection of the sides of the triangle SPS' on the asymptote gives
(r 8 + 2a 0 )cos(2z—z)—r„ cos z = 2a 0 . (23)
Adding r e to each side and using (21),
V 2 (l—cosz) = v 2 [l—cos(2z—z)].
(24)
EQUATIONS OF METEORIC MOTION
V. §4
Writing Az =
and
z—z
Vein J(z-f-Az) = vein J(z—Az)
tan JAz = tan Jz.
( 26 )
( 26 )
Thus, with v determined from (22), the correction Az to be added to
the observed zenith distance is obtained from (26). This correction is a
Fio. 48. The effect of zenith attraction.
maximum when the radiant lies on the horizon near the antapex when
it may approach 17°. Tables and graphs for the rapid determination of
the value of the zenith attraction in particular cases have been given by
several authors, such as by Hardcastle.f Davidson ,% and Nielsen.§
(6) Diurnal Aberration
A correction to the observed radiant must also be applied to allow
for aberration due to the rotation of the earth. If V E is the velocity of
the observer due to the earth’s rotation, and v the velocity of the meteor,
then the aberrational displacement K will be given by
k-5.
V
At latitude p, V E = 0-4639 cos ip km./sec. Thus
K = - 2 6 ' 58 008 ^ deg.
f Hardcaatle, J. A., J. Brit. Astr. Am. 21 (1910), 164.
x Davidson, M., ibid. 24 (1914), 307.
§ Nielsen, A. V., Mtdd. OU Rwner Obs. (1938), no. 12.
93
equations of meteoric motion
The displacements in right ascension (Ac) and declination (A8) are then
given by
Ac* =
AS =
26-58
v
26-58
cos ip . cos H. sec S,
cos ip. sin H. sin 8,
(27)
(28)
8 is the declination and H the hour angle of the radiant.
W Tto correction is small except for meteors of low velocity observed m
the region of the poles.
(r\ The True Radiant
( After correction of the apparent radiant for zemth “on and
diurnal aberration as described above the true radrant can be mutty
calculated In Fig. 47 if the elongation of the apparent radjant from the
a^xisM=RfiA), and of the true radiant «' (= TEA), then
(29)
W_
sine
V
sine'
sin(€'—«)
In the normal observational case v and e are measured. V is obtained
from (22), and then from (29)
cot*' = cote = -y cosec « (30)
and
V = V
sine
sine'
(31)
id) The Elongation of the True Radiant
The longitude (A') and latitude (/3') of the true radiant may be obtained
as follows. The right ascension (a) and declination (8) of the corrected
radiant are converted into longitude (A) and latitude (/3) by means of
the relations
cos/3.cosA = cos 8. cos a
cos/3.sinA = sinSsinc + cos8.sina.cosc , (32)
sin/3 = sinScosc — cos8.sina.sinc
where c is the obliquity of the ecliptic.
The positions of the apparent and true radiants (R and T of Fig. 47)
on the celestial sphere in relation to the sun S and apex A are shown in
Fig. 49. In the spherical triangle ARN
cos/3cos(A—A) = cose
cos/3sin(A—A) = sin€C09y
sin/3 = sincsin8 J
y
(33)
94 EQUATIONS OF METEORIC MOTION V, §4
from which c and y may be determined, c' is then given by (29) and the
spherical triangle ATN' solved by equations similar to (33) for A' and 0'
of the true radiant.
Fio. 49. The true radiant and orbital piano of the motoor.
5. Computation of the meteoric orbit
The computation of the elements of the meteoric orbit from the elonga¬
tion of the radiant and velocity have been described by many authors.
An account of the original methods of Schiaparelli and others is given
by Olivier.f Subsequent methods have been devised by Bauschinger.J:
Davidson,§ and others. The contemporary method used in the British
work is similar to that used by Laplace for cometary orbits and has been
described by Porter.|| It obviates the need for the solution of spherical
triangles by the use of direction cosines and is a considerable simplifica¬
tion on the older methods.
In Fig. 49 the great circle TS is the projection on the celestial sphere of
the plane of the orbit. Thus TSA = (180°—i) and the elements of the
orbit can be determined by the solution of the spherical triangle TSA.
Alternatively, in the method used by Porter equation (15) is rewritten as
= = (*')*+( 'yr+w. ( 34 )
where x', y', z' are the components of the meteor’s velocity—the earth’s
mean velocity being taken as the unit.
Then r 2 = x 2 -f y 2 -fz 2 (35)
and rr' = xx'+yy'-f zz'. (36)
t Olivier, C. P., Meteors, 1925.
X Bauachinger, J., Die Bahnbeslimmung der Himmelslc&rper, Leipzig 1928.
§ Davidson, M., J. Brit. Astr. Ass. 44 (1934), 110, 146.
|| Porter, J. G., Comets and Meteor Streams, Chapman & Hall, 1952.
v J# EQUATIONS OF METEORIC MOTION
Equations (10) and (11) may be written
95
ecosv
_P__
e sin v =
r
r'
(37)
(39)
Vp
p = V*r*-(rr') 2 - (38)
projection of twice the areal velocities on the planes of reference
are given by the standard equations
xy'-y*' = C i 1
yz*—zy* = C 2
zx # —xz # = C 3
These equations (39) determine the position of the orbital plane and
♦he other orbital elements are determined by equat.ons (34)-(38). The
H of the true anomaly v gives and the time of observation
gives^ The details of the procedure using this method have been
Len by Porter,t and also that of the reverse problem of determining
the radiant of a meteor moving in a given orbit.
f Porter, J.G., op. cit.
VI
THE DIURNAL AND SEASONAL
DISTRIBUTION OF SPORADIC METEORS
The number of meteors visible in a clear night sky to a single naked-eye
observer may be from 2 to 20 per hour. There is a diurnal and seasonal
variation, and the curve of variation is dominated by great increases in
activity at irregular intervals due to the occurrence of major showers.
These major showers are of paramount importance in meteor astronomy
and will be discussed separately. Nevertheless, owing to the short time
for which they are active, their contribution to the total number of
meteors entering the earth’s atmosphere during the year is considerably
less than the contribution from the sporadic activity. This chapter will
be concerned with these sporadic meteors. According to Prenticef the
activity outside the major shower periods is maintained by a large number
of minor streams (with rates not exceeding 1 per hour), as well as by
meteors, which as a result of perturbations are pursuing isolated paths
in space. It is unnecessary here to attempt such a distinction and we
shall refer to all meteors occurring outside the major showers listed in
Chapters XIII-XVIII as sporadic meteors.
1. The diurnal and seasonal variations of meteoric activity
The diurnal and seasonal variation of meteoric activity as found by
visual and radio methods is shown in Figs. 60 and 61 respectively. The
seasonal variations found by Wolf, Olivier, Denning, and Schmidt have
been markedly influenced by the occurrence of the intense Perseid
meteor shower in August. Even so, it is evident that all the results
indicate two marked features: (a) the activity is higher after midnight
than before, (6) the activity is higher during the second part of the year
than the first.
The explanation of these variations was first attempted by Schia¬
parelli l in 1866. If the meteor radiants were of uniform intensity and
were uniformly distributed over the celestial sphere, then, for an earth
at rest, the number of meteors visible at any point would be constant.
But the earth’s orbital motion will lead to an apparent concentration
of radiants around the apex of the earth’s way. This point lies on the
f Prentice, J. P. M., Rep. Phya. Soc. Progr. Phya. 11 (1948), 389.
X Schiaparelli, G. V., Note e Rifieaaumi auUa theoria aelronomica delle atelle codenti,
1866, translated into German by G. von Boguslawski as Entwurj einer ostronomiachen
Theorie der Stemachnuppen, 1871.
Hourly rate
AT ^Q •
Fio. 60. Diurnal variation <*”*”"*'a^ w ‘ th
a single run during 1947 Sept. 23-2 • Qng ^ tho roean observed hourly rates
the visual observations. The vwwl the data are as follows: Schmidt,
from a large number of obMrva ^. T f ^m ^formation given by Olivier, MtUors, eh.
Hoffmeister, c oulv.or G r a v ior--pl . {otuA froro information given by David-
,6 (Williams andWilkma. 1925). c B f%*. Soc. Proyr. PAys.
eon, M., J. BrU. Astr. Ass. 24 429 .
i > to » * •> °
- 00M* Ceohvr Cror* -*
HcfimeiUr-O--
■ Time UT
r\
A
/a;
/A
#
Mjy >*
*-• Hoffrnoster
~M H ~oi Hoy.
q — Courier <***r •— Wolf —
Sdwudt—m — flew** —©— £ * y * r
3595.66
98 THE DIURNAL AND SEASONAL VI, §l
ecliptic approximately 90° from the sun, and hence during the course of
the year its declination varies from —23-4° to + 23-4°. The correspond¬
ing altitude of the apex when it is on the meridian in latitude -f- 62 ° is
16° in spring and 61° in autumn. Similarly, the daily variation in the
same latitude is from — 38° in the evening to -f 38° in the morning. These
changes in altitude of the apex account qualitatively for the observed
diurnal and seasonal variation.
On the assumption of a uniform distribution of radiants of equal
richness the form of the variation can be derived as follows.f In Fig. 47
the earth’s direction and velocity is represented by V E and the meteors’
by V. Equation (29), Chap. V, then gives
sinfc'—g)
sin€
where c' is the true elongation of the radiant
from the apex and € the apparent elongation.
In Fig. 62 the earth’s orbital motion is along
CA (i.e. the direction of the apex), HIT being
the horizon. All meteor radiants above HIT
are visible and those below invisible. A
radiant just visible on the horizon at R
corresponds to a real radiant below the horizon at R' with t! given
by (1) above. Let <f> be the elevation of the apex above the horizon
(sin^ = sine in Fig. 62). Then
sin(c'—c) = ^sin <f>
and the meteors which are visible will come from the portion of the
heavens R'AR'. The height of the spherical cap R'AR' = r-j-r sin(€'— c)
is therefore proportional to sin^J and the area of the cap to
2w( 1 + yS“ 1 ^)-
Hence the ratio seen to the total number incident on the whole atmo¬
sphere will be
If we take the number in half the celestial sphere as unity, then the
f The flnnl result is the same as that given by Schiaparelli (loc. cit.), but the derivation
follows a method due to Davidson, M., J. Brit. Aatr. Asa. 24 (1914), 352.
VI|1 DISTRIBUTION OF SPORADIC METEORS •
nuffl her of radiants F seen when the elevation of the apex ^ -11 he
TT /OX
y
F = 1+Y sin ^
( 2 )
Schiaparelli tetter a»»»*l . P™** "W* te te meter. ..that
V = V2 .V b and F=l + ^sinf
The variation in the number of radiants with the elevation of the apex is
“Z ate™ exp— give tt. rmiatte m nemter
with i The number of meteors seen from a given radiant de P en ^" the
altitude of the radiant. Schiaparelli’s derivation of the correctedexp
sion for the number of meteor a visible is as follows. Theapexm
ecliptic with uniform motion at a distance of 90 behind the»sui> -
deviation of not more than ±1°. Choosmg zero epoch a . the “ F
solstice, the longitude A a of the apex will be nearly proportional
100
THE DIURNAL AND SEASONAL
VI, §1
and we can express the increment in time by dA a . In Fig. 64 PZM is
the observer’s meridian, with sun S, pole P, zenith Z, apex A, and
ecliptic ASM. Hour angle of the sun = H, with A 90° from S. It can be
shown that the angle APS varies from 94° 66' to 86° 04' and is given to
a close approximation by APS = 90°-f (4° 66')sin 2A a . Then APZ =
90°-f H-f-osin 2A a (where a = 4° 56'). In the triangle PZA, PZ is the
z
complement of the observer’s latitude (90°—0) and PA the polar distance
of the apex, given by
cosPA = sin A a sine, where c is the obliquity of the ecliptic.
The zenith distance of the apex ZA = z is then given by
cosz = 8in^co8PA-|-co8^8inPAco8(90 0 +H+a8in2A a ). (3)
The following approximations can be made:
sinPA = ^/(l—C 08 2 PA) = ^/(l—sin 2 A a 8in 2 c) = 1 —£sin 2 A a sin 2 €+...,
co8(90°-f H-fasin2A a ) = — sin(H-f asin2A a )
= — sin H—a sin 2A a cosH.
Then (3) becomes
cosz = sin ^ sin A a sine—cos 0(1 —£sin 2 A a 8in 2 €)(sinH4-sin 2 A a cos H).
(4)
In (2) let fi = V E /V, then since <f> = 90°—z,
l-f^sin0 = 1-f/xcosz.
The integral
then gives the mean number of meteors for the hour angle H at latitude 0.
Substituting cos z from (4) the integral reduces to
1 —ficos0sinH(l—£sin 2 c). (6)
Equation (6) gives the average mean frequency for all epochs and hours
of the day. If K is the mean hourly number of meteors seen throughout
VI § , distribution of sporadic meteors
the year, then the average number of those meteors observed in an hour
beginning (H-30“) and ending (H-f 30“) is given y
N = K{ 1 —M cos ^ sin H( 1 — i sin 2 e)}.
on the equator.
For the latitude of Greenwich (7) gives
N = K(l-0-598usinH).
181
2. Comparison of the observed diurnal variation with Schla-
parelli’s theory
Schiaparelli assumed that the meteors were moving at the parabolic
velocity limit so that V = V2. V E and M = 1/V2. Hence for the latitude
of Greenwich (8) becomes
N = K(l—0-42sinH). ( 9 )
The predicted diurnal variation plotted from (9) is shown in Fig. 55,
taking a mean absolute rate of unity. Also plotted in Fig. 55 are Den-
ning’sf observations made in the same latitude, reduced to the same mean
value. These observations are typical of the results on the diurnal varia¬
tion found by various observers and shown in Fig. 50. The agreement
between theory and observation is fairly good but far from complete. In
t See Fig. 50.
102
THE DIURNAL AND SEASONAL
VI. §2
particular the maximum in the observations occurs considerably earlier
than at 06h. as predicted by the theory. This discrepancy is evident in
all the observations of diurnal variation plotted in Fig. 60, including the
radio-echo observations which cannot have been influenced by dawn
light. We shall return to this matter in § 4.
3. Comparison of the observed seasonal variation with Schia¬
parelli's theory
From (5) the theory predicts the relative number of meteors observed
as the longitude of the apex varies from A fti to A ft| to be
V.
I (l-f/icosz) dA.
Introducing (4) this becomes
J {1+fz[sin sin A a sin c—cos ^( 1—j sin 2 A a 8in 2 c)(sin H sin 2 A a coeH)]} dA a .
( 10 )
By integrating between values of A a appropriate to the longitude of
the apex, eq. ( 10 ) gives the number of meteors to be expected at
different periods of the year for hour angle H. For our present purpose
it is sufficient to compare the average numbers predicted between the
summer and winter solstice (A* -► 0 to tt ) and between the winter and
summer solstice (A a -* n to 2n). In comparing the seasonal rates we
use the mean hourly rate averaged as H varies from 0 to 2 tt. Thus, since
2 n
f sin II dH = 0,
the theory predicts the ratio
mean hourly rate in second half of year _ N w _ l-K2/i/7r)sin0sinc
mean hourly rate in first half of year N s 1 — (2/z/7r)8in^8inc’
For the latitude of Greenwich
N w = 1+0-198^
N 8 “ 1-0-198^
and on the assumption of parabolic velocity (/* = 1/V2)
% =
The observed seasonal ratio found in the extensive observations of
De nnin g and his school averaged 2*1. The data have been treated by
VI 5 3 distribution of sporadic meteors 103
Davidsonf to remove ^mlnt wlthlpredicted value.
4 The discrepancy between theory and observation
laUff 8 von Niewlt investigated in some detail the discrepancies ^
exSed between the predictions of Schiaparelli’s theory and the ex'stmg
novations of the diurnal variation, particularly with regard to the
disagreement ^inieofm^Mium-
Xn^on a fro U mfhe apex but faded to obtain a satisfactory fit between
the theoretical and observed variations. The assumption o a value or
u > i/V2 that is of hyperboUc velocities for the meteors led to a better
agreement This suggestion, that the assumption of hyperbolic velocities
enabled the theory to be brought into better accord with observations
formed the starting-point of a protracted discussion as to the reality of
the hyperboUc meteor component. Essentially the dispute
the theory can be adapted to fit the observat.ons either by abandonmg
the assumption of random distribution of meteor paths and retaining the
paraboUc velocity limit, or by retaining a measure of random distribu¬
tion and exceeding the paraboUc velocity Umit. Unfortunately t has
not been possible to settle the dispute by an appeal to actual veloci y
measurements, since as discussed in Chapters VIII-XII, these measure¬
ments have themselves been the subject of severe disagreement. In this
chapter we shall proceed to discuss the measurements and interpretations
of the diurnal variation as given by Hoffmeister and by Prentice, which
iUustrate the two opposing views on this subject. FinaUy the recent
radio-echo investigations will be described.
5. Hoffmeister’s investigation of the diurnal variation
During the past thirty years a very great number of observations
have been collected by Hoffmeister, mainly under exceUent con¬
ditions in South Africa. The results, and Hoffmeister’s interpretation
of them, have been presented in two books;§ here we shall only
discuss Hoffmeister’s later views on the interpretation of the diurnal
variation.||
As regards the original work of SchiaparelU, Hoffmeister draws
f Davidson, M., J. Brit. Astr. Ass. 24 (1914), 478.
X von Niessl, Astr. Nachr. 93 (1878), 209. .
§ Hoffmeister, C., Die Meteors, Leipzig. 1937; Meteorstrdme, Weimar-Leipzig, 1948.
|| The author is indebted to Professor Hoffmeister for much discussion in correspon¬
dence and for the opportunity of studying his unpublished papers.
104
THE DIURNAL AND SEASONAL VI, §6
attention to additional factors influencing the observed daily variation,
particularly the effect of the acceleration due to the earth’s gravitational
attraction on the velocities, the effect of zenithal attraction upon the
radiants, and the inability to observe meteors at less than 5 ° altitude
even under good conditions. His fundamental expression for the
number of meteors observed per unit time at any point on the earth,
on the assumption of a uniform distribution of the original meteor
directions, is then Ar . r ..
N = f(z,fc,V), (11)
where z is the zenith distance of the earth’s apex, k the Average number
for z = 90°, and V the effective heliocentric velocity.
In 1931| Hoffmeister discussed the computation of k and V in detail
and pointed out that any shape of the diurnal curve might be possible
if the assumption of the uniform distribution of original directions is
abandoned. In other words any value of the velocity V derived from
fitting the observed variation curves with the theoretical ones, cal¬
culated on the basis of uniform distribution, cannot be regarded as a
real mean velocity, but rather as an apparent effective heliocentric
velocity whose variations with time and locality might give information
about the real distribution of meteor directions. Hoffmeister’s initial
extension of (11) took the form
N = Ar 1 [f(V)-f-f 2 (V)cosz-ff 3 (V)cos2z], (12)
where z is the zenith distance of the apex and k t = k the average
number of sporadic meteors for z = 90°.
The best fit with the observed material led Hoffmeister to conclude
that nearly 70 per cent, of the meteors made up a strong interstellar
component with a value for V = 206V E , instead of V = V2.V E on
the parabolic theory. However, his direct observations of a strong
ecliptical component,! the work of Whipple, and the day-time radio¬
echo observations on the short-period orbits in the ecliptical plane§ led
Hoffmeister to reinvestigate the distribution in order to test the effect of
including a particular ecliptical component in the sporadic distribution.||
His extension of (12) is then
N = ^ 1 [f(?)-ff 2 (V)cosz-f-f 3 (V)cos2z]-f fc 2 cosz e , (13)
where z 0 is the zenith distance of the ecliptical radiant and k 2 the
average of this component for z e = 90°. The problem now is whether
the inclusion of the ecliptical term enables the variation curves to be
fitted with a value of V > V2. V E . For this latest analysis Hoffmeister’s
f Hoffmeister, C., Verdff. Btrlin-Babelsberg, 9 (1931), no. 1. $ MtUorslrdme.
§ See Chap. XVIII. || Hoffmeister, C. Private communications (1951-2).
105
yI 5 6 distribution of sporadic meteors ^
observations were obtained under excellent c ° n ^ on ® m g hourly
long. 17° 5' E., lat. 22“ 35' S„ and include a total ot ,
numbers between 1937 April 30 and 1938 February^ J
fatigue, increase in brightness w.th velocity, and « ^ V *
brightness with increasing angular vetocity are cons.d tad ?
corrections. The last effect has been studied mgreatdetal by J
use of ‘artificial meteors'-t The treatment of the tW0 J
is as follows. IfiV m is the number of meteors between g . g
tudes (m—0'5) and (m+0-5) then the real distnbution func
given by fV m = f(m).4>(m),
where <*>(m) is a probability function. In order to evaluate *j?i p0 ° in t
meister assumed that within a certain area surrounding therwting P
of the eye aU meteors of a given magnitude will be seen, the areabeg
greater for brighter meteors. By concentrating on a very small area
the real distribution of different magnitudes will be seen, and by co
parison with general observation not restricted to this small area, *{m)
can be evaluated.
For <*>(m) Hoffmeister gives
m 0 1 2 3 4 6 6
4>(m) 1-00 0-95 0-78 0-51 0-25 005 0001
The values refer to a unit area of sky defined so that meteors of apparent
magnitude zero are seen without loss.
Table 11
Correction Factors in Hoffmeister's Analysis
Zenith distance
Zenith distance
of apex
of apex
deg.
Correction factor
deg.
0
1-456
90
10
1-396
100
1-339
110
1-285
120
40
1-232
130
60
1-182
140
60
MSS
150
70
1-087
160
80
1 043
170
90
1-000
180
Correction factor
1000
0-959
0-920
0-882
0-846
0-812
0-778
0-747
0-716
0-687
In order to obtain a final correction curve it is necessary to make
assumptions about the change of angular velocity during the night and
the distribution of angular velocities. Hoffmeister uses his own values
t Meteorslrome.
106
DISTRIBUTION OF SPORADIC METEORS
VI. §6
and those of Opik derived from the rocking mirror observationst and
gives the final correction factors of Table 11 to be applied to observed
meteor frequencies.
Hoffmeister divided his observational material into nine groups as
follows:
Group
1
2
3
4
6
6
7
8
9
DM
1937 April 30-May 22
May 27-June 20
June 25-July 20
July 25-Aug. 18
Aug. 24-Sept. 17
Sept. 22-Oct. 16
Oct. 22-Nov. 16
Nov. 20-Dec. 15
Dec. 19-1938 Feb. 5
Sun's longitude
deg.
40-62
66-89
94-118
122-146
161-175
179-203
209-233
238-263
267-317
The meteor counts in each group are divided into eight to eleven mean
values for different zenith distances. Meteors identified as belonging
to known showers are excluded. The nine curves of diurnal variation
thus obtained are shown in Fig. 56 compared with the theoretical curves
computed for uniform heliocentric velocity of V = 2-5V E . Except
for groups 7, 8, 9, the departures are considerable, but Hoffmeister
points out that the discrepancies can be explained by a superposition
of the classical variation curve with a secondary curve possessing a
maximum after midnight. This indicates the effect of the ecliptical
component, its decline in groups 7 to 9 being due to a real decrease of
the average k 2 and to the change in the meridian zenith distances of
the radiants. These curves, therefore, demonstrate that without the
introduction of corrections due to the ecliptical component the new
observations indicate a high heliocentric velocity in complete agree¬
ment with Hoffmeister’s previous conclusions from earlier observations.
Now on the basis of (13) Hoffmeister gives a least square solution
for k v k 2 , and V with the following results:
Group
v/v E
*i
1
211 ±0-40
9*80±1*90
2*78±2*34
2
2*23±0*22
8*75±1*14
3*88±1*42
3
208 ±0*19
8-99±0-42
4*0
4
205±015
10*84±0*36
60
5
1*98±0*36
8*16±1*40
3-34±l*86
6
2*04±0*24
8-41±0-86
212±1*31
7
1*55±0*22
10*70±1*00
9*46±1*78
8
1*60±0*25
12*76±1*93
3*93±3*73
9
1*48±0*26
812±0*53
3*0
t See Chap. IX.
Fio. 56. Curves of diurnal variation of meteors as obtained by Hoffmeister
from visual observations in latitude 22° 35' S. The nine curves correspond to
approximately equal intervals from 1937 April to 1938 Feb. (see text). The
broken curve is the theoretical variation on the assumption of a uniform helio¬
centric velocity of V = 2-5V e .
THE DIURNAL AND SEASONAL
VI, §6
108
A comparison of the average number k 2 of ecliptical meteors (radiant
in zenith) with former direct observations of this componentf serves as
a check on the computation. In the case of groups 3,4, 9, it was necessary
to use the previously observed value for k 2 .
Hence, even when allowance is made for the strong ecliptical com¬
ponent, the value of V still emerges as distinctly hyperbolic though
smaller than previously, its mean being V = 1*90±0*09V E .
Hoffmeister then subtracts the ecliptical component by normalizing
according to N DOrm = (N co „’-k 2 co3z)ki 1 . The resultant mean corrected
curves for groups 1 to 6 (May to October) and groups 7 to 9 (November
to January) are compared with the theoretical variation curves in
Figs. 57 and 68. In Fig. 58 the theoretical curve for V = V2.V E agrees
well with the corrected observational curve, and hence the results for
the period November to January are in agreement with the parabolic
theory. On the other hand the results for May to October (Fig. 67)
indicate a markedly hyperbolic velocity (V ~ 2-0V E ).
It will be scon laterj that the most recent velocity measurements
fail to demonstrate the markedly hyperbolic component required by
the above analysis. The question therefore arises how Hoffmeister’s
observational data, to which great weight must be attached, can be
aligned with these results. Hoffmeister offers the following possibilities:
(i) the data used on the velocity-luminosity relation, and the
decrease of apparent brightness with increasing angular velocity, may
be wrong. This would influence the correction factors listed on p. 105.
(ii) The deviation of the curve in Fig. 57 from the parabolic form
might be compensated by an opposite deviation during the other part
of the year. Hoffmeister’s own southern hemisphere observations
during March and April 1933 are irreconcilable with this possibility.
(iii) There may be another component with direct motion, thus
requiring a further term in (13).
Hoffmeister gives reasons why it is unlikely that any such features
could markedly influence the results; nevertheless the more recent
results obtained both by the visual and radio analysis of the sporadic
distribution indicate that either (i) or (iii) or a combination of both
must have influenced Hoffmeister’s analysis.
6. The distribution of sporadic meteors according to Prentice
The investigation of the sporadic distribution made by Hoffmeister
discussed above is based on meteor counts, but the true path of the
X Chap. XII.
f MeUorslrdmt.
VI, §6
distribution
OF SPORADIC METEORS
109
Fio. 68. The average valuee of groups 7 to 9 of Fig. 86 compared with the
theoretical variation curve assuming a parabolic velocity V = vz. v B .
individual meteors remains unknown. Clearly a more direct attack on
the problem of specific components in the sporadic distribution can be
made if the true paths of the individual meteors are observed. This has
been achieved by Prentice,! with members of the B.A.A. network of
no
DISTRIBUTION OF SPORADIC METEORS
VI, §6
meteor observers, using a visual technique in which the individual
meteors are observed from two points on the earth’s surface as described
in Chapter II.
An observer O x> Fig. 69, recorded the path of a meteor using the
stellar background as a reference guide. In this way a plane was defined
which contained the meteor path and the observer. The intersection of
this plane with a similar plane recorded by another observer 0 2 defined
the path of the meteor in the atmosphere. These planes when projected
on to the celestial sphere form great circles as shown in Fig. 60, the
intersection of which defines the apparent radiant of the meteor.
The results of these observations are shown in Figs. 61 (a) and 61 (6).
The distribution in ecliptic latitude (Fig. 61 (6)) shows that the sporadic
meteors are largely concentrated in the plane of the ecliptic. The
longitude distribution in Fig. 61 (a) shows a concentration from the anti-
helion point at least as great as that from the apex of the earth’s way.
These directions may be visualized more clearly with the help of Fig.
62 which shows the earth’s orbit EXYZ. The concentration in latitude
is along QR with the maximum in the plane EXYZ. The concentrations
in longitude, in the plane EXYZ, lie along the apex of the earth’s way
(EA) and towards the antihelion point EP. These results demonstrate
in a striking manner the error in the original assumption of Schiaparelli
that the meteor radiants are uniformly distributed. Before discussing
the implications of these results we shall describe the radio-echo work on
the sporadic meteors which confirms and extends these visual observa¬
tions to the day-time sky.
t Prentice, J. P. M. (in preparation).
(*)
Fio. 61. The distribution of sporadic meteors as derived from duplicate visual
observations by Prentice.
(а) Distribution of visual radiants in local ecliptic longitudo.
(Abscissa: longitude A-sun’s longitude ©.)
(б) Distribution of visual radiants in ecliptic latitude.
Fio. 62.
112
THE DIURNAL AND SEASONAL
VI. §7
7 . The radio-echo investigation of the sporadic distribution
The radio-echo apparatus designed for the continuous investigation
of meteoric activityf has been used by Hawkins and AspinallJ to study
the distribution of the sporadic meteors. As described elsewhere! this
equipment uses two aerials beamed in azimuth and directed at 26° N.
and S. of West respectively. On the radio frequency used (72 mc./e.)
the radio reflection from the meteor trails is aspect sensitive, and hence
Fio. 63.
only those meteors whose paths lie in a restricted volume of space will
be recorded at any given time. In Fig. 63 the observing station is at E.
ABCD is the celestial sphere and ANCX the horizon circle. The beamed
aerials are directed along EG and EH respectively. If the aerial EG
produced an infinitely narrow beam, directed horizontally, then only
those meteors would be recorded with paths in a vertical plane perpen¬
dicular to EG. The combination of finite beam widths, slight elevation
of the maximum lobe, and a restriction on range measurement to 1,000
km., finally yield a collecting volume enclosed between two planes such
as XOY and XO'Y, with a similar arrangement for EH as at X'OY',
X'O'Y', the inclination between the two sectors being that of the
aerials, that is 50°. The effect of the diurnal rotation of the earth can
most easily be visualized as a rotation of the celestial sphere ABCD,
with E and the sectors fixed. It will be seen that every day each of the
aerials takes a complete sample of the meteor activity in the northern
hemisphere. For example, meteors with paths lying in a plane through
the apex will be recorded in the aerial EH when the apex is within the
f See Chap. IV. $ Hawkins, G. S., and Aspinall, A. (in preparation).
distribution of sporadic meteors
X'OO'Y', than UUr, wl.n th- ^
aerial EG when the apox is within the sector XOO .
Oct. 1949
April 1950
00 06
Sector I °-
16 18
Sector 2
12 16
Hours (U.T)
Fig. 64 (a). Monthly means of tho diurnal variation of sporadic metoor radiants
as measured by the radio-echo technique during the period 1949 Oct.-19uO Sept.
known meteor showers are eliminated from the records the distribution
of the sporadic meteor directions can be obtained.
The mean monthly diurnal rate curves for both sectors are shown
in Fig. 64 (a) for the year 1949-50, and in Fig. 64 (6) for the year 1950-1.
114
THE DIURNAL AND SEASONAL
VI, §7
The average of all the monthly curves throughout the year is shown in
Fig. 65 (a) (corresponding to Fig. 64 (a)) and in Fig. 65 (6) (corresponding
Fio. 64 (6). Monthly means of the diurnal variation of sporadic meteor radiants
as measured by the radio-echo technique during the period 1950 Oct.—1951 Sept.
to Fig. 64 (6)). The displacement of the maximum in these curves is a
result of the inclination of the two aerial beams. Figs. 66 (a) and 66 (6)
(corresponding to 65 (a) and 65 (6) respectively) give the means of the
separate curves for the two sectors corrected for this inclination. These
curves represent the distribution of the sporadic meteor activity in
longitude and may be compared with the results of the visual observa¬
tions shown in Fig. 61 (o). Both the radio-echo and visual observations
show nearly equal concentrations towards the apex and antihelion points.
THE DIURNAL AND SEASONAL
VI, 5 7
116
Fio. 66. The mean of the curves for the two sectors, combined by correcting
for the inclination of the collecting areas: (a) corresponding to Fig. 64 (a);
(6) corresponding to Fig. 64 (6).
Abscissae: (longitude A—sun’s longitude ©).
In addition, the radio-echo observations extend into the daylight sky
and show a similar concentration towards the helion point (EH in Fig.
62) . The radio-echo observations do not give a distribution in latitude
to be compared with Fig. 61 (6), but the results can be satisfactorily
V, , , DISTBIBTJTION OB plane
interpreted in terms of ^ e C " Ration of 24° can be obtained
in FiK- 61 (&)• A mean v 1 1 tw0 aerial beams as shown
from the displacement of the^ ^ dijeothm 0 f the heUon, anti¬
in Fig. 66, that is from th ® a0t1 ^ att ain their maximum elevation-t
helion, and apex pomts when J latitude in the plane of
Thus, if this activity was also be expected to be 23’
the echptic, the measured decimal genera! agreement
:r s ass- -«— 18 near the
■ a a • 1 ana
wxvu *-
ecliptical plane.
Surety I
Sumy 2
R'
Fio. 67. Distribution of apparent
radiants in local longitude.
8 . Th.«. tzzl * «...... ^
From the results described §§ ofbits ^ latitude most of
the true distribution of spora p i an e of the ecliptic. In
the orbits he in a ‘^^^SeoorLate. around the earth
l0Ilg hown toFig^'l “rh® distribution of sporadic orbits may be obtained
are shownm Jig. b7. xa orbital motion in the following
"°" tu. by . cil0l ,V represent, the horiton of »n
tion « 0 is given by ^ = c+sin -i^ sint ). (H)
t See Chap. IV, where the application of the apparatus to determine the declination of
the shower radianta is described.
118
VI, §8
THE DIURNAL AND SEASONAL
These radiants are located in a sector dc', where
dc
d?
V
V
W-
V isin*«).
V 2
(15)
An increase in the apparent velocity V' increases the number of inter¬
cepted meteors, so that the true density in space is proportional to
v _
V' V(V*+VH- 2 W E C 08 *„)•
( 10 )
Fio. 69. Distribution of orbital directions of sporadic meteors.
By taking the parabolic limiting velocity for V, the distribution of Fig.
67 can be corrected for the earth’s motion by using the above equations.
The corrected distribution is given in Fig. 69. It represents, for any point
in the earth’s orbit, the number of meteor orbits which cross in any speci¬
fic direction. The distribution indicates a preponderance of directly
moving meteors. Some indication of the actual orbits of these meteors
can be obtained by using the velocity measurements of the sporadic
distribution during the summer months.f These show that the meteors
are moving in orbits of high eccentricity similar to the orbits of the
intense summer day-time streams.!
It is therefore evident that the original assumption of uniform distri¬
bution made by Schiaparelli has little relation to the true distribution.
Finally, it is necessary to inquire if the true distribution as now derived
is capable of yielding the form of the diurnal variation curve observed
by Hoffmeister without the assistance of hyperbolic velocities. If the
f See Chap. XII.
x See Chap. XVUI.
1 IQ
yI§8 DISTRIBUTION OF SPORADIC METEORS
radiants are assumed to ^ ^^^f^therate" a* any instant
*•**• of w-o). - <™ +s ,, t wh.„.»
may be found by summation, N 2 /< , f 20°
the number of visible positions on the^ediptie Fig . 70
curve of diurnal variation for latitude
o 2 o S « 5 ) compared with the appropriate diurnal rate curve calculated
22 1 5 r m the intensity of the various components as measured
“ itSJ 53 “ N^ The sudden decrease in activity shown by the visual
How values of z is due to the decrease of visibility at dawn. The
addition of this directly moving component of high eccent ™'J{|
Hoffmeister’s analysis (§ 5) can also explain his observations with
reference to the hyperbolic component.
The general agreement is so good that there no longer seem to be
anv grounds for the introduction of a hyperbolic component in the
sporadic distribution. It will be seen in Chapter XII that the most
recent measurements of the velocity distribution of sporadic meteors also
fail to reveal any velocities in excess of the parabolic limit.
Prentice, J. P. M, Rep '^ 8 'J' ion 9 due io the zenith attraction, and the allowance
for the SCI 1 "/the meteor layer on the effective collecting area of the observe.
120 THE DIURNAL AND SEASONAL VI, §0
9 . The seasonal variation of sporadic meteor activity
In § 3 the observed seasonal variation was compared with Schiaparelli’s
theory with only fair agreement. In the light of the foregoing it will
FiQ. 71. The seasonal variation of sporadic meteor activity to be expected if
the sporadic meteor orbits are uniformly distributed around the earth’s orbit.
Comparison with the observed seasonal variation (Fig. 64) indicates a marked
asymmetry.
be apparent that no close agreement could be expected, since the true
distribution of sporadic meteors is markedly different from the uniform
distribution assumed in the original theory. The new results on the latitude
and longitude distribution can be used to predict the seasonal variation
VI59 DISTRIBUTION OF SPORADIC METEORS
(6) The variation of cometary index with sun’s longitude O .
uniform. From the mean distribution around the earth as shown in
Fig. 69, the seasonal variation to be expected is obtained as in Fig. 71.
The monthly averages are represented by the area under each curve, and
122 DISTRIBUTION OF SPORADIC METEORS VI, §9
these can be compared with the actual observed monthly averages of
Fig. 64. It is evident that the discrepancies are considerable and hence
that the density of meteor orbits around the earth’s orbit is far from
uniform. A measure of the irregularity can be obtained from the ratio of
the observed monthly averages (Fig. 64) to those to be expected on the
assumption of uniform density (Fig. 71). This ratio is plotted throughout
the year in Fig. 72 (a). The surprising feature of this distribution is that
the activity is much higher in the summer (region of O = 90°) than in the
autumn—a result in direct contradiction to the prediction of Schiaparelli’s
theory, and to the visual observations restricted to the night-time sky.
The density of the sporadic meteor orbits in the region of the earth’s
orbit, around O = 90°, evidently more than compensates for the low
altitude of the apex. Also plotted in Fig. 72 (6) is the index computed
by Herschcl and Hoffmeister.f proportional to the number of comets
crossing the earth’s orbit and their closeness of approach. The agree¬
ment of these curves, and the occurrence of the high-density sporadic
meteoric orbits of direct motion and high eccentricity in the same region
of the orbit as the intense summer day-time streams, is very suggestive
and will be discussed in Chapter XXI.
t Hoffmeist*r, C., McUoretrime, 1948.
VII
the number and mass distribution
OF SPORADIC METEORS
nnR Dresent knowledge of the total numbers of meteors entering the
stse: —. or sii
Which can bo observed at any given time depends on the length ol the
meteor path and hence upon magnitude. Further corrections
necessary to join the visual and telescopic magnitude scales and for the
correction of the magnitude of meteors which are observed other than
in the zenith.
1. The effective field of view for telescopic observations
The effective field of view for telescopic observations is greater than
the normal visible field because of the finite length of the mcteor paths.
Thus, amongst the meteors counted will be those whose P oult3 of °"^
lie outside the visible field, but subsequently move into it. In tog.
the circle of radius D/2 represents the normal field of view of the telescope.
Meteors of path length L originating outside this field may move into
it and the effective field can be calculated as follows. Consider an
element AB of length (D/2) 8y on the circle bounding the field of view of
the telescope. Some of the meteors of path length L originating in the
element PQRS (area x S{ 8x) will pass through AB and en ^ r ^‘« field
of the telescope. The angle subtended by AB at PQRS is - and
the ratio of the number of meteors passing through AB to the total
number from PQRS will be Hence the total number of
meteors of path length L originating outside the field of view and sub-
sequently entering it is given by
L 2 n +lw
= DL.
x=0y-0
f Watson, F., Ann. Harv. CoU. Obs. 105 (1937), 624; Proc. Amer. Phil. Soc. 81 (1939),
493.
124
THE NUMBER AND MASS DISTRIBUTION OF VII, §1
The effective field of view for meteors with path length L is therefore
given by
Fio.l74. Schematic representation of the total collecting area
(«D*/4 + LD) for telescopic observations of metoore when L > D.
The area available for the beginning points of metoore which
cross the field is vertically ruled.
F 10 . 75. Schematic representation of the total
collecting area (trD*/4+LD) for telescopic ob¬
servation of metoore when L < D. The area in
which meteors both begin and end in the field
is cross-hatched.
This expression was first deduced by Opik.f Following WatsonJ this
additional ‘rectangular invisible’ field DL can be represented diagram-
matically as in Figs. 74 and 75.
t Opik, E., Publ. Tartu 06s. 27 (1930), no. 2.
X Watson, F., Proc. Amer. Phil. Soc. 81 (1939), 493.
126
VII, §2
SPORADIC METEORS
2 . Probability =! ob.erva.i.n of different
Z; ^ ™ w » “■ si ““* to ™ b, °
field is a smaU fraction of the total field,
P« = Pe =
ttD 2 /4
r W D
ff D J /4+DL "D+ 4L_
jizxsssssxxxz -=
cross the field: .
f ?-1 (?-H
p c - 4 (l)/4)(nU-i-4L)
= 4 -vD + 4L
4L—wD
For L ^ D,
Pn =
ttD+4L'
T(H^
p — Lll
‘BE
(D/4)(7rD+4L)
= 2
Dsin-’lg
7rD-p4L
This vanishes when L > D.
Since meteors which both begin and end in the field will also be
counted as either beginning or ending in the field:
Pb+Pe+Pc-'Pbe =
The probabilities that meteors with various values of L/D will be observed
in these categories has been computed as above by Watsont and the
results are given in Table 12 and Fig. 76.
f Watson, F., loc. cit.
126 THE NUMBER AND MASS DISTRIBUTION OF VII, §2
Table 12
Probabilities of Telescopic Observations for Various Values of L/D
L/D
Pjj and Pg
Pc
P BB
Area of
effective field
Increase in area
for doubled D
00
10
0-0
10
10
4-0
01
• •
• •
0-775
• •
0-2
0-803
0-003
0-609
1-26
3-32
0-3
• •
• •
0-451
..
0-4
0-663
0-005
0-333
1-51
3-00
0-6
..
• •
0-237
• •
• •
0-6
0-669
0-016
0-154
1-76
2-78
0-7
..
• •
0-097
• •
..
0-8
0-497
0-062
0-056
2-02
2-66
0-9
• •
• •
llKaM 1 ! 1 / ’ MS# 1 11
..
10
0-440
0-120
0 000
2-27
2-66
1-25
0-386
0-228
• •
2-69
• •
1-6
0-344
0-312
• •
IfPm z
2-42
1-76
0-310
0-380
• •
3-22
• •
20
0-282
0-436
• •
3-54
2-32
2-6
0-239
0-522
• •
418
• •
30
0-207
0-686
• •
4-81
2-22
3-6
0-183
0-634
• •
6-45
• •
40
0-164
0-672
• •
6-10
218
60
0-135
0-730
• •
7-35
216
Fio. 76. Probability P of observing meteors of path length L with
a telescopic field of diameter D. BE paths beginning and ending in
the field. C paths which cross the field. B, E paths which begin or
end in the field.
There data were used to determine the average path length for
meteors of given brightness.
VII, §3
SPORADIC METEORS
127
3 . The observational data
(a) Counts and Path Lengths
The observations were made in 1934 at an elevation of 6 000 ft. m
south California using a 4-in. telescope mounted horizontally wit
45 “ mirror in front of the lens for observing the meteors in the zenith.
From'star visits the field diameter was found to be
The magnification was 18 giving an observer s eye field of 66 ^ameter.
The effective field of view for different magnitudcs was determined y
observing the distances of the beginning and ending ,points of
from the centre of the field. The results were as shown in Table 13.
Table 13
Effective Field of View for Different Meteor Magnitudes
Apparent magnitude .
Diam. of effective fiold .
Diem, of effective eyo fiold
< 3
3-5
220'
140'
66°
42°
4-5
80'
24°
The numbers of meteors in the various categories outlined in § 2
were then counted for field diameters of 220' (66°), 110' (33°), 55' (16-5 )
and Fig. 76 used to determine the path lengths. The total numbers of
all categories observed for various field diameters are given in Table 14.
Table 14
Number of Meteors as a Function of Field of View and Magnitude
Apparent
magnitude
Frequencies for fields of
Rat
ios
220' (N fc )
110' (N b )
55' (N c )
NJN b
N b /N c
1- 5
2- 5
3- 5
4- 5
11
29
49
85
7
22
36
62
12
15
25
l-6±0-8
l-3±0-4
l-35±0-3
l-37±0-2
• •
1- 81 ±0-7
2- 40±0-8
2-50±0-6
Some of the ratios NJN b and N b /N c fall below 2, indicating that the
effective field diameter was less than that used to obtain the ratio. These
ratios can also be used to estimate the path lengths by using the last
column of Table 12. The accuracies are rather low, the path length for
different magnitudes varying as shown in Table 15 amongst the four
different derivations.
128 THE NUMBER AND MASS DISTRIBUTION OF VII, §3
Table 15
Path Length of Meteors as a Function of Magnitude
App. mag.
Path length from Fig. 76
Path length from
Table 12, column 6
220'field
110 ’field
55' field
1-5
630'
• •
• •
2-5
926'
• •
• •
• •
3-5
240'
105'
160'
80'
4*6
06'
33'
44'
60'
(6) Magnitudes
In order to combine the results with the naked-eye observations it
was necessary to associate the two scales of magnitude. During the
telescopic observations simultaneous observations were made in the
zenith by a naked-eye observer, and in a number of cases faint meteors
seen by the naked-eye observer were observed in coincidence with the
telescope. The results are given in Table 16; together with the results
of similar observations made by Opik.f
Table 16
Correlation of Naked-eye and Telescopic Magnitude Scales
Naked-eye
magnitude
Telescopic magnitude
El
El
-0-6
10
1-5
20
2*5
10 .
1
1
• •
• •
• •
• •
# #
• •
H
1-5 .
• •
• •
• •
• •
• •
• •
T
• •
20 .
• •
• •
• •
• •
• •
• •
• •
1
2-6 .
• •
• •
• •
• •
• •
• •
• •
• •
30 .
• •
1
• •
• • I
• •
1
• •
• •
3-6 .
• •
• •
• •
• • '
1
1
• •
• •
40 .
• •
• •
• •
• •
• •
3
1
1
T
Total coincidences
Telescopic but not
1
H
0
0
N
6
1
2
?
naked eye
Fractions obs. by
• •
• •
• •
2
4
7
17
naked eye
10
• •
• •
10
0-71±0-6
0-25
0-22±014
T
Opik's ratio
Mean naked-eye
10
• •
• •
0-02
0-60
• •
0-21
• •
magnitude
1
H
• •
••
3-5
3-7
4
4
• •
The magnitude correction scale was extended to the eighth magnitude
by observing the apparent magnitude of faint stars in the telescope;
beyond, extrapolation was necessary to the limiting magnitude (tenth).
The final correction curves used are shown in Fig. 77.
t Opik, E., Publ. Tartu Obs. 25 (1923), no. 4.
VII, §3
SPORADIC METEORS
129
4 The frequency of different magnitudes
The final results of the work of Watson can be combined as in lables
17 and 18. The mean path length is taken from Table 15 and the adjus -
ment to kilometres made by assuming a height of 86 km. with no
allowance for projection effects.
The total observing time was 1,529 minutes. Correcting for the
difference between this and the length of a day (1,440 minutes), and using
the data in Tables 17 and 18, gives the data shown in Table 19 for the
numbers of meteors of different magnitudes entering the whole earth s
atmosphere daily.
Table 17
Path Length and Effective Area of Visibility for Meteors of Different
Magnitudes
Magnitude
Path length
Apparent
1- 5
2- 5
3- 5
4- 5
True
4- 5
5- 8
7-5
9-5
Min. of
arc
500
500
160
50
Km.
12
12
50
1-3
Effective
field diain.
220 '
220 '
140'
80'
Effective area
Sq. min.
15 X 10 4
15
3-8
0-9
Fraction of
atmosphere
18x 10
18
4-6
M
35M.66
K
130
THE NUMBER AND MASS DISTRIBUTION OF VII, §4
Table 18
Number of Meteors of Different Magnitudes
App. magnitude
No. of slow
i
1
00
10
20 1
2-5
30
36
Q
B)
meteors .
No. of medium
1
H
0
3
1
1
0
D
D
moteors
No. of fast
2
l
D
2
6
15
17
20
28
moteors
□
11
n
□
4
1
1
3
6
9
19
□
Table 19
Numbers of Meteors of Different Magnitudes entering the Earth's
Atmosphere per Day
True magnitude .
n
4
5
□
7
8
9
10
Numbor
28
63
Ej
292
790
2,240
(1.660) xl 0 «
Log N
7-47
7-72
QZj
8-47
8-90
9-36
(923)
The change in numbers dN with magnitude dm appears to be of the
form dN = x” dm. (1)
The base x is the increase in numbers per magnitude, and in the present
case has a value of about 2-5 when averaged over the range of magnitudes
given in Table 19. At the ninth magnitude some 2x 10 9 meteors per
day enter the atmosphere. The figures for the tenth magnitude cannot
be regarded as complete since this is near the limiting magnitude for
the observations.
5. Other observations of the frequency distribution
In an earlier analysis of the problem Watsonf used data obtained
by Opikt and Boothroyd§ during the Arizona Meteor Expedition. He
selected those meteors which were then recorded as having hyperbolic
velocities in order to derive the mass distribution in interstellar space.
It is now believed that these hyperbolic velocities were erroneous,||
nevertheless this fact does not significantly influence Watson’s analysis.
Boothroyd§ listed 707 telescopic observations of which 488 were selected
as having angular velocities 3 deg./sec. in excess of the parabolic limit.
OpikJ: listed 279 naked-eye observations of which 133 were selected as
having heliocentric velocities greater than 50 km./sec.
f Watson, F., Ann. Harv. Coll. Obs. 105 (1937), 623.
J Opik, E., Circ. Harvard Coll. Ob$. (1934), no. 389.
§ Boothroyd, ibid., no. 390.
|| See Chap. XII.
131
vn §5 SPORADIC METEORS
The observations described in §§ 1-4 were made in the zenithal direc¬
tion In the present observations corrections have to »* •»£££
observed magnitudes since the observations were not restricted to
the zenith. Since meteors observed at low alt.tudes may e a ^
siderable distances from the observer it is necessary
observed magnitudes to the zenith where they become comparable.
Fio. 78. Curve for correction of observed meteor magnitudes to zenithal
magnitudes.
Boothroyd’s telescopic observations were at 45° to the zenith and a
constant zenithal correction of -0-76“ was applied. For the naked-eye
observations the corrections derived by Opikf and plotted in Fig. 78
were applied. The various other corrections for field of view of the
telescope and the change of field diameter with brightness as described
in §§ 1-4 were also applied. The results for the daily frequency over the
entire atmosphere for the different magnitudes are plotted in Fig. 79.
Also plotted are the later results of Watson (from Table 19), and other
data by Opik and Hoffmeister. Opik’sJ results were obtained from an
investigation of the luminosity function of Perseids and non-Perseids.
Watson assumes that the non-Perseids were interstellar meteors, and
t Opik, E., Publ. Tartu Obs. 25 (1923). no. 4. 70.
X Opik, E., ibid. (1922), no. 1.
132
THE NUMBER AND MASS DISTRIBUTION OF VII, §5
that the observers in all cases watched the same area of sky. The results
of Hoffmeisterf are from a list of 4,478 naked-eye observations made
over a period of two years. Watson adjusts Hoffmeister’s magnitude
scale so that the fifth magnitude was the limiting magnitude, and not
the sixth, as given by Hoffmeister.
(plotted from Table 19).
Probably not much weight can be attached to the difference in
numerical magnitude between the results of Watson, Opik, and Hoff¬
meister since the data from the two latter have not been taken from a
specific investigation of daily frequency. The agreement between the
slope of the various curves is satisfactory. According to McKinley,!
Millman has determined the distribution from 1,938 visual observations
made on clear moonless nights by a team of six observers. The slope of
the curve from magnitude —3 to +3 is similar to those of Fig. 79 and
t Hoffmeister, C., Ver6ff. Berlin Babelsberg, 9 (1931).
X McKinley, D. W. R., Canad. J. Phys. 29 (1951), 403.
133
SPORADIC METEORS
V XX o o
. v.l». of , in equation (!) of 2-7, whiefc »i» »“**>'’'
ment with Watson’s value of 2-5. constant
"" * ditoTf- ft.7.“S£i. ~ .yatentatie trend, U» value of »
——
of 1 between magnitudes + 1 ana + ai . 0 f
magnitudes + 3 -^ ^
Ve 7d b th 8 e h thJoreUcal frequency distribution of photographic meteors,
Sfrl rphotographs in the magnitude
by M Using
naked-eye and binocular observations he first established that the valu
oft had the same value at two points on the magnitude scale separated
by 5 or 6 magnitudes. Two short magnitude intervals were chosen for
comparison where the various selective processes could be •«!»*"*to
be the same. The value of x obtained was 2-29±0-16, but W,lham
considered that this could have only small we.ght owing to preferentia
selection Ho therefore chose observations from the binocular senes
best suited to a determination of x on the assumption that it was constant
over the magnitude range. From the original observations, wW*e
made by Knabe,|| Williams selected meteors such that the initial point
were not greater than 3° from the centre of the field of view, at which the
observer's eyes were directed. The magnitude estimate corresponding
to maximum light was adopted. Table 20 was thereby obtained, show¬
ing the frequency of initial points/for meteors of apparent magnitude m,
at distances R from the centre of the field.
The unit of area is taken as that for R = 0-5°, which is almost exactly
the area observed by the macula lulea region in the retina of the human
eye. The column F shows the frequency reduced to equal areas for
meteors brighter than +8 mag. The decrease is almost linear as ono
recedes from the foveal region of the eye. Williams considers that the
decrease is not due to lack of sensitivity outside the foveal region, but
more probably to lack of attention as one recedes from this region. In
view of the smaU size of the sample and of the roughness of the run in
+ Millman, P. M. ( Proc. Nat. Acad. Sci. Wash. 19 (1933), 34.
1 Millman, P. M., J. Roy. Aslr. Soc. Can. 29 (1935), 210.
§ Williams, J. D., Astron. J. 48 (1939), 100; Proc. ^Imcr. Phil. Soc. 81 (1939), 505,
Astrophys. J. 92 (1940), 424.
|| See Williams, J. D. (1939), ibid.
134
THE NUMBER AND MASS DISTRIBUTION OF VII, $5
frequencies Williams obtained the most probable value of x for each
zone by an objective method of maximum likelihood due to Fisher.f
Table 20
Frequency of Meteors as a Function of Magnitude in Williams's
Analysis
If the magnitude range is cut into s+1 intervals by the points
—co, m 0 , m 0 +Am, m 0 +2Am,..., m 0 +$Am = m'
then the probability of finding a meteor in the sample whose magnitude
lies in the (i+l)fch interval is
m.+tAm
Pi = A J e mm dm (i = 1,2,...*),
m«+(<—l)Am
m*
and p 0 = A J e“ m dm (e* = x),
— co
m'
where A is fixed by the normalization 1 = A j e ,m dm. a has to be
— CO
determined in terms of the observed frequencies /< (i = 0,1,...,*). It can
be established that the likelihood of the sample
P = Urt
0
is a maximum when
cothJaAm = 1 +]yZ^[ N * - 2 */<]-
where N is the total observed frequency, a result obtained when the
logarithmic derivative of P with respect to a is equated to zero. This
f Fisher, R. A., Proc. Comb. Phil. Soc. 22 (1925), 700.
135
SPORADIC METEORS
™L- o P , ta ».—. -- - -—“
estimated from d 2 log P\\~i 2 sinh£aAm
°“ = L \-da^)J “ Am^W-Po)}*
E bJM. tie op.»tlon of the m.» ™<»- I»».
are give/in Table 20. The combination leads to a va u
h = 208±010.
The computed frequencies compared with the observed are given in
Table 21 ’ Table 21
Comparison of Observed and Computed Meteor Frequencies as a Function
F of Magnitude in Williams s Analysis
m .
Observed
Computed
m .
Obsorvcd
Computod
^o^esult^jTthese^various observations is that the three most direct
investigations of the frequency distribution give values of x of 2 7
(Millman), 2-5 (Watson), and 2-08 (Williams) in the visual^
infra-visual magnitude range, while there is some evidence that for
very much brighter meteors the value of x is 3-5 (Millman). The position
is not satisfactory, but there is good hope that in the near future
radio-echo techniques may be used to determine an independent.value.
A method depending on the measurement of the height dntntotwa
is described in Chapter XIX in connexion with the frequency distnbut.on
of the shower meteors. Preliminary application of this method to the
sporadic distribution gives a value of x = 2-5.
6. The mass distribution
Since the magnitude of a meteor is proportional to the logarithm ot
the intensity, which, in turn, depends directly on the mass m, equation
(1) for the frequency distribution of magnitudes becomes
dN = ^ p
m p
136 THE NUMBER AND MASS DISTRIBUTION OF VII, § 6
for the mass-frequency distribution. The exponent p is related directly
to the base x of equation (1). For a likely value of x = 2-5, the exponent
P = 2, and the mass distribution follows an inverse square law.
In this section we shall be concerned with the actual meteoric mass
entering the atmosphere in the various magnitude groups. Uncertainties
in the mass estimates arise because of the incomplete state of the meteor
evaporation theory. Whereas the relation between luminosity, mass,
and velocity can be expressed as
/ = const, xm Xv* = 10-°- 4x < ma e>.
( 2 )
the possible values for the exponent s vary over a wide range. Thus
Opikf originally proposed a value for s = 2-5, which has been adopted
by WatsonJ in his work on the mass distribution. In his full theory,
however, Opik§ deduces s = 3, but more recently|| concludes that
8 < 1. Similar uncertainty exists over the mass to be attributed to a
meteor of given magnitude, but according to current ideas the original
calculations of Opik§ indicating a most probable mass of 12 milligrams
for a Perseid meteor of second magnitude appears to be approximately
correct.
By substitution in (2), taking s = 2-5 and v = 56 km./scc., WatsonJ
evaluated the constant as 5-64 xlO- 7 , giving the equation for mass
determination in the form
Mass (mg.) = 1-77 x l^XlO-^^xv* 6 . ( 3 )
For the extreme limits of s = 1 to s = 3 the respective equations are
Mass (mg.) = 4-25 X 10 3 x v 1 , (4)
Mass (mg.) = 1-33 X 10 7 x lO-o ^^x v 3 . (5)
Thus taking Opik’s figure of 12 mg. as the most probable mass of a
second magnitude Perseid meteor moving with a geocentric velocity of
56 km./sec., equations (4) and (5) give the mass limits in Table 22 for
meteors of various magnitudes moving at the parabolic limiting velocity
(72 km./sec.).
f Opik, E. J., Circ. Harvard Coll. Obs. (1930), no. 355.
x Watson, F., loc. cit.
§ Opik, E. J., Pull. Tartu Obs. (1933), no. 26. (Harvard Reprint, no. 100.)
|| Opik, E. J., Observatory, 68 (1948), 229.
137
VII, §6
SPORADIC METEORS
Table 22
Magnitude
Masa (mg.)
eq. (4)
Moss (mg.)
eq. (5)
*
1
2
raw —
3
4
5
6
7
8
9
23-5
9-35
3-7
1-48
0-59
0-23
0-093
0-037
0-014
11-3
6-66
2-25
0-89
0-35
0-14
0-056
0-022
0-0089
__ j
10
00059
00036
Watson reduced his data to total masses ' '
osep.ntine the geocentric velocities, which extended from 20 to 220
Z C l real. Velocities in excess of the parabolic limit are not now
believed to existf and hence it seems more satisfactory to reduce Watson s
utr data given in Tabic 19 assuming that aU the meteors are moving
Uh velocities near the parabolic limit and using the mass. of
Table 22 The results for the total daUy mass intercepted by the earth s
atmosphere for the magnitude range 1 to 9 are given in Table 2£ for the
two assumptions about the velocity term. Also included are Watson s
result^ 3 using the v« term, including his analysis for the presumed
velocities up to 220 km./sec.J
T.iii v 91
Daily Mass of Sporadic Meteors intercepted by the Earth as a Function
of Meteor Magnitude
Magnitude
1
2
3
4
5
6
7
8
9
2 Mass mag¬
nitudes 1 to 9
inclusive
2 Mass using
oq.(4)
(X 10 T rog.)
4-7
1-88
2-22
4 15
3-1
3-3
2-7
2-9
3-1
2-8 X 10*
2 Mass using
oq. (5)
(x 10 T mg.)
2-3
M3
1-35
2-5
1-8
2-0
1-6
1-7
1-8
1-6 x 10*
2 Mass,
Watson
(xlO 7 rog.)
013
019
0-20
0-72
0-53
1-4
20
1-2
(1-6)1
0-8 x 10 *
| Mean of 7 and 8.
In view of the uncertainties in the work the agreement is rather good.
Even the difference between the extreme assumptions of the hyperbolic
theory (last line) and the parabolic theory leads to no more than
a factor 4 of uncertainty in the total daily mass for nine magnitudes.
Greater importance must be attached to the first two estimates as based
on more recent observations by Watson and calculated in line with the
parabolic theory. A figure of 2x 10 7 mg. per magnitude per day over
t Seo Chap. XII. t Wats0 ". F - loc - cit -
138 THE NUMBER AND MA88 DISTRIBUTION OF VII, §0
the entire atmosphere is probably correct to within a factor of 10 even
allowing for uncertainties in the basic assumption of 12 mg. for the mass
of a second magnitude Perseid meteor. It will be noticed that, although
for each fainter magnitude there are about 2-7 times as many meteors
(Table 19), the total mass in each magnitude remains constant.
Table 23 has been restricted to magnitudes 1-9 as representing the
limits included in Watson’s later observations. Watson’s earlier analysis
of the Arizona dataf extended to magnitude —3 and indicates that the
same mass distribution will be appropriate. There does not appear to
be any published investigation of the magnitude ranges outside these
limits of —3 to + 10, although Watson^ assumes that the relation will
hold from —10 to +30. At the brighter limit the meteors will penetrate
to the earth as meteorites, and the estimated mass falling per day is
660 kg.§ At the faintest limit the particles will be too small to enter
the atmosphere, being dispersed by radiation pressure from the sun.||
Table 24 summarizes these various estimates of mass and energy
brought into the atmosphere assuming the meteors move at the para¬
bolic velocity limit.
Table 24
Mass and Energy brought into the Earth's Atmosphere by Sporadic
Meteors
Meteors
Total daily mass over
earth's atmosphere (kg.)
Total energy
per day (ergs)
(a) > — 10 mag.—based on meteorite
falls.
650
13-0x 10»
(6) —4 to —9 mag.—extrapolation
from (c).;
120
3 X 10 w
(c) — 3 to + 9 mag.—observational data
(Table 23).
200
6-6 X 10W
(d) +10 to +30 mag.—extrapolation
from (c).
400
10 0 x low
Total.
1,330
3-2x10“
7. The space distribution
From the above data it is possible to calculate the density of meteoric
matter in the solar system. The number of meteors swept up in time t
by the earth will be those contained in the cylinder of volume
Tzrftv,
where r t is the radius of the earth’s atmosphere (6,400 km.) and v the
f Watson, F., Ann. Harv. Colt. Obs., loc. cit.
X Watson, F., Between the Planets (Blakiston, 1948).
§ See Chap. XIX. || See Chap. XX.
139
SPORADIC METEORS
J ’° li 3 f^Table 23 we have deduced that the meteoric mass swept up
“17” 77«e i. «x» B - Thu. a. -P— —V '■
2-5 X 10- 11 cm. /km . 3 /magnitude
— 2-5 X 10- 26 gm./c.c./magnitude.
The distribution of space
from the information given
density in the various mass groups derived
in the previous tables is shown in Table 25.
Table 25
Space Distribution of Sporadic Meteor Material
Meteor magnitudes
Mas* range of
individual particles
Number per
day
Mass per day
Number
per c.c.
Density
gm./c.c.
/— 10 to -8
Extra- 1—7 to — 6
potation
/ 0 to +1
Obsorvft- 2 to 4
tional 5“
data 7 to 9
V 10 to 12
Extra- ( 13 to 20
polation l 21 to 30
500 to 100 gm.
100 to 10 gm.
10 to 1 gm.
1 gm. to 100 mg.
100 mg. to 10 mg.
10 to 1
I to 0 1
0-1 to 0 01
0 01 to 0 001
10 "* to 10 "*
10 "* to 10 -»
~ 300
~ 2.500
~ 1-8.10*
~4.10»
10*
3 6.10 1
1 9.10*
3-3.10*
0-5.10‘*
~ 10’*
~ 10**
~6.10* gm.
~ 4.10*
~ 4.10*
- 0.10*
4.10*
0 . 10 *
4.10*
6.10*
6.10*
16.10*
18.10*
4.10"**
3.10"*’
2.10"**
6.10"“
1-5.10"“
4 5.10-”
2 4.10"“
4-1.10-“
8-1.10-“
- io-“
~ 10-*
7-5.10~“
6 0.10-“
5 0.10"“
7-5.10"**
5-010-“
7-5.10"“
5-0.10-“
7-5.10 “
7-5.10"”
~ 20.10"“
~ 20.10-“
In the range of masses from 1 gram to 1<H mg. (- 3 to +12 magnitude)
the space density is about 8-5.10-“ particles per c.c. and the mass
density about 4 x 10-“ gm./c.c. These figures are probably reliable to
within a factor of 10. The extrapolation to larger and smaller limits
assumes that the same distribution applies as in the observed magnitude
ranee and must be regarded as somewhat uncertain. If these are included
the density increases to about 10-“ gm./c.c. These figures are of the
same order as those obtained by Watsonf using the Arizona data and
allowing for the presumed hyperbolic velocities.
It is of interest to compare these figures with the density of matter
in interstellar space, which is believed to be between 10~“ and 10 “ gm../
c.c.J This is the same range of densities indicated above for the meteoric
matter in the solar system. The absorption measurements indicate that
these interstellar particles have radii of 10-* or 10-* cm. giving masses
of less than 10-“ gm. Such particles, which lie well below the mass limit
t Watson, F., Ann. Harv. Coll. 06s., loc. cit.
X Centennial Symposium (Harvard, 1948).
140
THE NUMBER AND MASS DISTRIBUTION
VII, §7
of 10 -11 gm. considered here, would not be expected to appear as meteors
in the earth’s atmosphere.
The data considered in this chapter refer only to sporadic meteors.
During the occurrence of the intense meteor showers these numbers
and densities will be increased. This subject will be considered in
Chapter XIX.
VIII
the velocity of sporadic meteors I
INTRODUCTION AND THE VON NIESSL-HOFFMEISTER
INTRODUL FIREBALL CATALOGUE
pfiuation (16) of Chapter V the limiting or parabolic
velocity of a meteor of mass m at a distance r from the sun is given by
V‘=Y (M+m)|, M
wh ere v is the constant of gravitation and M the mass of the sun If
S r we write the mean distance of the earth from the sun, then the
limiting heliocentric velocity is
V p = 421 km. /sec.
The question as to whether the velocities of sporadic meteors exceed
this limit, and therefore have an interstellar origin, has provoked a major
discussion in meteor astronomy. Tins problem arose in Chapter VI m
connexion with the diurnal variation in sporadic meteor rates. In
next five chapters it will be discussed on the basis of the actual measure¬
ment of meteor velocities. There are at least three major difficulties
which give rise to the uncertainty in providing a clear-out answer to this
problem:
(а) None of the existing methods of velocity measurement (Chapters
II and IV) except the photographic, can provide a sufficiently precise
measurement of an individual meteor velocity ; and so far the photo¬
graphic measurements have been restricted to comparatively small
numbers of bright meteors. ...
(б) The velocity of a particle moving through space, at rest with
respect to the sun, would be 20 km./sec. Further, it is known that the
peculiar velocity of interstellar clouds relative to the sun is small,
amounting to 10 km./see. or less.t Hence it is reasonable to assume
that the resultant velocity v of an interstellar particle in the solar
system would be of the same order as that of the sun through space, that
is 20 km./sec. The heliocentric velocity V of such a particle at the
t Adams, W. S.. As,r. J. 97 (1943), 105; Whipple F. L CltoioI Symposium
(Harvard, 1946). p. 110; Greenstein, J., Astrophysics (McGraw Hill, 19o2).
142
THE VELOCITY OF SPORADIC METEORS—I
VIII
distance of the earth from the sun will be given by
V 2 = \2_\2
( 2 )
or V = 46-6 km./sec. for v = 20 km ./sec. Thus the most common
interstellar particles would be expected to exceed the parabolic limiting
velocity by only 10 per cent.
(c) The heliocentric velocity cannot be measured directly, but can
only be inferred from a measurement of the geocentric velocity, v. For
this to be done it is necessary to measure the spatial path of the meteor
as well as its velocity, in order to allow for the earth’s orbital motion
and the gravitational attraction of the earth on the meteor. The velocity
of a meteor in free fall (neglecting air resistance), which is initially at
rest, reaches 1M km./sec. due to the earth’s attraction. The correction
for this alone varies from 1 to 5 km./sec. in the extreme cases of head-
on and approach from behind, respectively.
1. The von Niessl-Hoffmeister fireball catalogue
If the length of the meteor path is divided by the time of flight and
if the height is known, an estimate of the geocentric velocity of the
meteor can be obtained. From such estimates Brandes and Benzenberg
of Gottingen first decided that meteors were extra-terrestrial bodies.
Since the estimates of duration (a fraction of a second) are very uncertain,
the derived velocities are liable to gross errors. In the case of fireballs,
or very bright meteors, the position is better because of the much greater
length of the visible trail and the longer duration compared with ordinary
meteors. The famous Katalog der Bestimmungsgrdpen filr 611 Bahnen
grofier Meteore by von Niessl and Hoffmeisterf was compiled from such
observations and has given rise to protracted discussion, because 79
per cent, of the fireballs are listed as possessing hyperbolic velocities.
The catalogue is a critical selection from the available data on bright
meteors. After von Niessl’s death the catalogue was completed by
Hoffmeister to No. 518. The list to No. 611 was added by Hoffmeister
from unfinished discussions and new data. Of the entries in the catalogue
283 are from English observers,I 23 from America, and 71 from von
Niessl’s recomputation of other British data.§
f von Niessl, G., and Hoffmeister, C., Denksch. d. Akad. d. Wise. Wien, Math.-Naturw.
(1925), 100.
X Herechel or Denning 268, Tupman 10, Glaisher 1, Crumplen 1, Davidson 3.
§ From the Reports of the Committee on Luminous Meteors of the British Associa¬
tion for the Advancement of Science.
VIII, 5 2 VON NIESSL-HOFFMEISTER CATALOGUE
2, Fisher’s first criticism
The conclusion in favour of such a high perccnlage of hyperbol c
velocities was first criticized by Fisher, t who assembled^firebaU hs s
from four other sources in addition to the catalogue, in order to compa
the seasonal trends, Fisher's sources were as foUows the sequence
corresponding to the respective plots m Figs. 80 84.J
(i) Personal observations of 168 fireballs between 1841-53 by
Coul vier-Gravier;§
(ii) personal observations of 987 fireballs between 1876-1925 by
Torwald K 0 hl;||
(iii) 1,500 cases compiled from the literature (excluding (i) and (n))
in Prior’s Catalogue of Meteorites, Eastman’s Progress of Meteoric
Astronomy in America, VAstronomie, Bulletin de la SocidU
Astronomique de France, del el Terre, and the AI scries of the
Harvard photographs;
(iv) 285 cases from the Harvard meteor photographs (not entirely
independent of (iii));
(v) the von Niessl-Hoffmcister catalogue (not entirely independent
of (iii), although it contains only 23 examples from America).
The rate plots from these five sources are shown in Figs. 80-84,
takon from Fisher’s work, the year being divided into seventy-three
groups of five days each. In the case of Fig. 84, for the von Nicssl-
Hoffmeister catalogue, the velocities (hyperbolic or non-hyperbohe)
aro also indicated. From a comparison of these rates Fisher formed the
opinion that there was a definite periodicity in the arrival of fireballs
and hence that their frequency depended on the position of the earth
in its orbit. Also in Fig. 84 the frequency of the presumed hyperbolic
velocities follows the same periodicity. Now, if there are 79 per cent,
interstellar particles in the sample their distribution would be expected
to be random. Fisher draws particular attention to the minimum around
Juno 19-24 at sun’s longitude 90°. He considers that the two possible
influences on the randomness—the sim’s motion and the possibility of
interstellar streams—could not be responsible for the patchiness and that
the clustering in the radiants of the fireballs, shown in Figs. 85, 86,
and 87,t indicates that they are associated with well-known shower
radiants with elliptic or nearly parabolic velocities. But the computed
t Fisher, W. J., Circ. Harv. Coll. Obs. (1928), no. 331.
t Figs. 80-87 are taken from Fisher, W. J., ibid.
§ Coulvier-Gravier, F. A.; F. Arago. Astronomie Populaire, 4 (1857), 275.
|| Torwald Kohl, Nordisk Astronomisk Tidsskrift, 6 (1925), 97.
fCO 200 300 Oa/s
I Jan I Feb I Mar. I Apr I May I June I July I Aug I Sept I Oct. I Nov I Dec. I
Figs. 80 84. The fireball rotes throughout the year as found by: (80) Coulvier-
Gravier; (HI) TorwaM Kohl; (82) Miscellaneous catalogues (see text); (83)
Harvard meteor photographs; (84) von Nicssl-Hoffmcister fireball catalogue.
• hyperbolic velocities. X less than hyperbolic. O undetermined.
145
VIII 5 2 VON NIESSL-HOFFMEISTER CATALOGUE
Fia. 85. Radiants of tho fireballs in
the von Niessl-Hoflmeistcr cataloguo
between Oct. 14-25 plotted in ecliptic
coordinates. The f Ariotid radiant
(see Chap. XV) is that given in Den¬
ning's catalogue, no. xxvi.
Fio. 86. Radiants of tho firebulls in
tho von Niossl-Hoffraeister catalogue
between Nov. 5-25 plotted in ecliptic
coordinates. Tho < Taurid radiant
(seo Chap. XV) is that given in Den¬
ning's catalogue, no. liii.
Fio. 87. Radiants of the firoballs in the von Niessl-Hoffmeistcr cataloguo
between Dec. 8-16 plotted in ecliptic coordinates compared with the Gominid
radiant (seo Chap. XV).
heliocentric velocities of von Niessl and Hoffmeister for these three
groups are mostly hyperbolic as shown in Table 26.
Fisher also attempted to show that there must be a systematic error
in the observations leading to an overestimate of geocentric velocities.
However, Maltzevf pointed out that his basic equation contained an
error in sign, which vitiates the argument and no purpose would be
served in reproducing it.
f Maltzov, V. A., Mon. Not. Roy. Astr. Soc. 90 (1930), 568.
L
3595.66
146
THE VELOCITY OF SPORADIC METEORS—I VIII, §2
Table 26
Velocities in Fireball Catalogue for certain Radiant Clusters treated by
Fisher
Fig. 85. Oct. 14-25.
Fig. 86. Nov. 6-25.
Fig. 87. Dec. 8-16.
Heliocentric
Heliocentric
Heliocentric
No. in
velocity
No. in
velocity
No. in
velocity
catalogue
( km. j sec.)
catalogue
(km./sec.)
catalogue
(km.jsec.)
392
38
427
82
pEp
77
406
49
428
58
49
409
• •
429
39
45
410
60
431
67
• 0
411
62
434
80
495
97
412
60
437
57
497
82
440
9 •
601
94
442
49
36
443
99
498
38
457
..
600
66
462
47
602
64
465
37
466
45
467
41
468
• •
470
51
3. Maltzev’s analysis
Maltzev further objected to Fisher’s assumption that, because of the
association with known radiants, the velocities must be less than
parabolic, citing the beliefs of Kleiber f and von NiesslJ that these were
actually interstellar streams. We shall see in Chapter XV that the
subsequent accurate velocity measurements showed that the presumed
hyperbolic stream in Taurus is actually a stream in a short-period
elliptical orbit. Maltzev then analysed the heights of appearance and
disappearance of the fireballs in the von Niessl-Hoffmeister catalogue.
His results are shown in Fig. 88, from which he concluded that the
heights of appearance and disappearance increase with the geocentric
velocity and that the appearance of ordinary shooting stars is 20-30
km. lower and the disappearance 20-25 km. higher than that of the
hyperbolic fireballs. From a further analysis Maltzev concluded that
for equal geocentric velocities the heights of appearance and disappear¬
ance depended on the heliocentric velocity of the fireballs. These data
were all considered to be in favour of the hyperbolic fireball theory.
t Kleiber, J. A., The Astronomical Theory of Shooting Stars (St. Petersburg, 1884).
t von Nicsal, G., Encyklop. d. math. Wissensch. vi (2), 10 (1910), 464.
VIII, §3
VON NIESSL-HOFFMEISTER CATALOGUE
147
Fio. 88. Maltzov’a analysis of the mean height* of appouranco (•)
and disappearance ( X ) of the firoballs in tho von Niessl-Hoffmeistor
catalogue. Tho number of cases used is indicated beside oach plot.
4. Fisher’s second criticism
Shortly after the publication of Maltzev’s work Fisherf produced
further evidence that the velocities in the von Niessl-Hoffmeister
catalogue must be overestimated. He effectively carried out a test,
first suggested by Galle in 1874, in which the velocities of meteors belong¬
ing to well-known elliptical orbits, such as the Perscids and Leonids,
are measured by the same visual technique and compared with the fire¬
ball catalogue. Fisher therefore collected observations (mostly from
British sources to agree with the preponderance of data used in the fire¬
ball catalogue) on the Quadrantids, Lyrids, Perscids, Orionids, Leonids,
and Geminids: all being meteor showers with generally acknowledged
closed orbits. The data collected by Fisher from these sources is plotted
in Figs. 89 and 90 for each of the showers and for the fireball catalogue,
as a function of velocity against path length. The slant lines through
the origin are the loci of points for which velocity and path length corre¬
spond to durations of \ sec., 1 sec., etc., as marked. The points with
serial numbers also appeared in the fireball catalogue and those marked
H were quoted as having a hyperbolic velocity. From these figures
Fisher draws three conclusions, (i) The plots tend to group along lines
of equal duration (notably 1 second)—a result due to observational
t Fisher, W. J., Circ. Harv. Coll. 06s. (1932), no. 375.
148 THE VELOCITY OF SPORADIC METEORS—I VIII, §4
convenience since generally estimates, as distinct from measurements, of
the time of flight were used, (ii) The spread of path lengths and velocities
for equal observed durations is very great, and does not improve for long
flights. The same is true of the spread with regard to the periodic
velocity, (iii) Nearly all the points above the line of periodic velocity
would mean hyperbolic heliocentric velocities, were the meteors not
otherwise identified as belonging to circumsolar streams. Thus 61 per
cent, of the Leonids would have been judged to be hyperbolic meteors
on this criterion, and certain Perseids, Orionids, and Geminids actually
appear as hyperbolic meteors in the fireball catalogue. A further analysis
of the data is given in Table 27.
Again it is evident that the means found from the observational path
length/time of flight data tend to exceed considerably the geocentric
velocity of the shower meteors. Thus Fisher concludes that, since
the visually observed periodic meteor velocities are unreliable and high,
Fio. 90.
Fios. 89 and 90. Fishers data on the visually observed meteors from the
Lyrid, Orionid, Perseid, Geminid, Leonid, and Quadrontid streams as ft
function of velocity against path length. Where there is ambiguity the smglo
numbering indicates the duration groups (c.g. 2). The mult.p 6
indicates that the meteor vras actually used in the von N,e ^ 1 "^, offme ' bt ^ r
catalogue (e.g. 503 = no. 503 in tho catalogue. 490 h = no. 490 (hyperbolic
velocity).
150 THE VELOCITY OF SPORADIC METEORS—I VIII, §4
the von Niessl-Hoffmeister catalogue velocities with the same range of
durations must be equally unreliable and high, with the probability
that the same defects must influence others of longer durations.
Table 27
Comparison of Velocities of Meteors belonging to known Showers compared
with the Values given in the Fireball Catalogue
Streams
So. plotted
in Figs.
89 and 90
No.
tabulated
Spread
km./sec.
Arithmeti¬
cal mean
Harmonic
mean
Median
Geocentric
velocity
estimated
from
stream
period |
Quadrant ids.
21
22
21-85
45-1
41*8
42-65*
Lyrida
15
15
31-80
55-9
63-1
54-6
47* 1§
Pereeids
145
147
68-1
63-6
04 4
61-25||
Orionids
15
16
652
62-7
65-2ft
Leonids
31
38
75-6
71-4**
Geminids
16
18
24-113
121
48-3
43-6tt
t The velocities quoted here are thoso used by Fisher, and are not necessarily the
values now accepted. For example, tho Gominid volocity is now known to be
35 km./sec. (seo Chap. XV) and this still further strengthens Fisher’s argument.
X Kirkwood, D., Proc. Amer. Phil. Soc. 13 (1873), 501.
§ Maltzev, V. A., Mirovedin* Astr. Bull. (1929), no. 24, 1.
|| Velocity assumed parabolic,
tt Kirkwood, D., Proc. Amer. Phil. Soc. 11 (1871), 229.
XX Newton. H. A., and Adorns, J. C., Amcr. J. Sci. 37 (1864), 377; 38 (1864), 53;
Mon. Sot. Roy. Astr. Soc. 27 (1860-7), 247.
5. Later discussions of the fireball catalogue and Watson’s
analysis
Following Fisher’s second criticism Maltzevt made a further analysis
of the harmonic mean velocities and concluded that they were principally
hyperbolic. Knopf X plotted the distribution of apparent radiants and
believed that he had evidence for the activity of streams in Taurus and
Scorpius throughout the year, thus indicating that they were truly
interstellar. On the other hand Wylie§ concluded from the study of several
well-observed fireballs that the paths given in the fireball catalogue
were too long, which would mean that the derived velocities were too
high. If Wylie’s belief is correct then the high altitudes given by Maltzev||
for the appearance of the fireballs can be explained.
f Maltzev, V. A., Tashkent Obs. Bull. (1934), no. 3, 57.
x Knopf. Astr. Sachr. 242 (1931). 161.
§ Wylie, C. C., Pop. Astron. 43 (1935), 241, 312, 379, 602, 657; 44 (1936), 42, 162;
45 (1937), 101, 209.
|| Maltzev, V. A., Mon. Sot. Roy. Astr. Soc. 90 (1930), 568.
151
m , . VO* h,« S sl-ho,™«s TE * —'
2S2MS- «
sr„r^ir-=r^-/v, - »> -
jB
apparent radiant at elongation € U> the apex, then
to correct the apparent radiant is given by
30 .
sin(A<) = -^sin«,
the di*—being^along
50 < V.
Table 28
Watson'. Analysis of the Distribution in latitude of Velocity Groups in the
Fireball Catalogue
Mid-latitude of zone
V< 43
43 < V < 50
50 < V
—
5°
15°
33%
20
40%
12
45%
18
25°
15
20
9
35
11
14
9
45°
10
5
9
55*
7
5
2
65°
2
1
5
75°
2
2
2
85°
0
1
1
In Kg. « .her. » seeenit grouping, wbi.h nhghj. Morale ■
of fireballs—particularly those at a 160 , 8 +5 , a 1 <o > + ■ ’
8+2°. The latter is the ‘Scorpius stream’ with a mean hc l0Ce " t l
velocity of 51 km./sec., agreeing with the concentration as selected by
t Watson, F., Proc. Amer. Phil. Soc. 81 (1939), 473.
152 THE VELOCITY OF SPORADIC METEORS—I VIII, § 5
von Niesslf in Scorpius. Watson tested the significance of these group¬
ings by applying Poisson’s equation
P(N) =
where N 0 is the average number of radiants per unit area and N is the
anticipated number. Between latitudes 0° and -f 10° there are 141
Fio. 92. Distribution of space radiants from the von Niossl-Hofhnoister
catalogue as plotted by Watson.
radiants which, when considered over 36 intervals, 10 degrees wide,
gives N 0 = 3-91. The number of the 36 intervals N in which we expect
to find N radiants is compared with the observed number in Table 29.
Table 29
Results of Watson’s Test of the Significance of Apparent Radiant Groups
in the Fireball Catalogue
N
P( N)
S expert#!
51 obs.
N
P(N)
N expected
N o6s.
srm
0024
0-9
2£ 1*4
5
0-15
5-6
g&X
i
0090
3-3
2£l-4
6
0-094
3-5
fruit
2
0 17
6-4
4 £20
7
0-050
1-9
3
7-9
8£ 2-8
8
0-018
4
7 £2-6
Table 29 gives no indication that the groupings are anything but
accidental. Finally Watson made a similar reduction for the radiants
found in the Arizona Meteor Expedition,J assuming parabolic velocity,
t von Nienl, G.. Sit:, d. k. Akeul. d. Wist. WUn, 121 (1912), 1925.
X Circ. Harv. Colt. Ob*. (1934), no. 388.
VIII, §5
VON NIESSL-HOFFMEISTER CATALOGUE
163
F,o 93. Watson's analysis of the distribution of space radiants of meteors
P observed during tho Arizona expedition.
With the result shown in Fig. 93. The concentration towards the ecliptic
compared with the concentrations in the fireball catalogue are listed in
Table 30.
Table 30
Comparison of Concentration of Meteors in the Arizona Results unth those
in the Fireball Catalogue
Mid-latitude .
6°
15°
25°
35°
46°
65°
65°
75°
85°
Concentration in fire¬
ball cataloguo .
41%
17
12
11
8
4
3
2
1
Concentration in Ari¬
zona results
33%
14
16
13
6
4
7
6
1
On the whole the fireball radiants are even more concentrated towards
the ecliptic than the Arizona radiants, which almost certainly had
periodic orbits. Hence there are only two possible conclusions: either
(a) the fireballs are from interstellar space and just by chance have
motions principally in the ecliptic like the periodic streams, or (6) the
velocities in the fireball catalogue are not significant and the fireballs are
actually members of the solar system like the periodic streams.
6. Summary of discussions on the von Niessl-Hoffmelster
fireball catalogue
In the above sections some examples have been given of the discussions
which have centred around the velocity data in the von Niessl-Hoff-
meister catalogue. Evidently an appeal to further measurements is
necessary before any decision on the validity of these measurements
154
THE VELOCITY OF SPORADIC METEORS—I VIII, §6
can be taken. Even Opik, who from his measurements (described in
Chapter IX) firmly believed in the hyperbolic theory, nevertheless
doubted whether the velocity data in the catalogue were well founded, f
In a critical analysis of British meteor data Porterf showed that little
reliance could be placed on the paths of the meteors observed by Denning
or Herschel. Hence, since 44 per cent, of the paths in the fireball cata¬
logue are from this source, Porter§ considers that the velocity data in the
catalogue are essentially unreliable. On the other hand there are one or
two cases of observations of meteorites or fireballs by reliable observers
which indicate a marked hyperbolic velocity. Perhaps the most famous
of these is the case of the Pul tusk meteorite which fell on 30 January
1868, where the two principal observers were an astronomer and a
trained army officer. In his analysis of the data, Galle|| found the velocity
to be hyperbolic. The conditions were unusually favourable since the
meteorite was overtaking the earth. The average observed velocity
was 28 km./sec., corresponding to an average duration of 6-7 sec. derived
from 26 estimates. From this material Galle derived a marked hyperbolic
heliocentric velocity of 57 km./sec. For a parabolic velocity the duration
would have to be doubled. More recently the case of the Pultusk meteorite
has been thoroughly discussed by Nielsen,ff who again arrived at the
conclusion that the velocity was hyperbolic; the revised heliocentric
value being 56 km./sec. giving an interstellar velocity of 37 km./sec.
t Opik, E., Irish Astr. J. 1 (1950), 84.
X Porter, J. G., Mon. Sot. Roy. Astr. Soc. 103 (1943), 134.
§ Porter, J. G., ibid. 104 (1944), 257.
|| Galle, J. G., Abh. Schles. GeseUschaJt. Sat. u. Med. (Breslau, 1868).
tf Nielsen, A. V., Meddel. OU Rommer Obs. (1943), no. 17.
IX
THE VELOCITY OF SPORADIC METEORS—II
THE WORK OF OPIK
The rocking-mirror apparatus designed by Opik has been described in
Chapter II. It was used by Opik and his colleagues to measure meteor
velocities during the Arizona Meteor Expedition! (1931-3), and after
1934 at Tartu in Esthonia. A meteor seen in the mirror describes a
cycloid. This curve was redrawn as it appeared visually and the angular
velocity was calculated by two methods: (i) from the shape of the
trajectory (w x ), (ii) from the observed length and duration as given by
the number of the loops ( w u ). The heights and paths of the meteors
were obtained from simultaneous observations by two observers
separated by about 40 km.J In the final reduction of the data to linear
velocities, however, mean heights were used, because the spread in
meteor heights was found to be smaller than the observational error
in the observed heights.
1. Treatment of data
The systematic and accidental errors were estimated from meteors
belonging to specific radiants where a parabolic velocity could be
assumed (in the later reductions a correction for the probable ellipticity
of these meteors was introduced.) For example, in his reduction of some
of the preliminary data§ Opik took sixty-four stream meteors and
divided them into two groups according to geocentric velocity, as shown
in Table 31.
Table 31
Opik's Preliminary Grouping of 64 Stream Meteors
Mean geocentric velocity v, km./sec..
36
71
Number of heights......
22
16
Harmonic racan|| height of trail centre h, km. .
70-0
85-8
Probablo error in mean height, km. .
±20
±3-7
Because of the small change in height with velocity, and because
the real spread is of the same order as the observational errors, Opik
t Shapley, H., Opik, E. J., and Boothroyd, S. L., Proc. Nat. Acad. Sci. Wash. 18
(1032), 16.
t See Chap. H. § Opik, E. J. t Circ. Harv. Coll. Obs. (1934), no. 389.
|| Harmonic mean heights are computed in this work instead of arithmetical means
because the observational errors are in parallax, and because a mean angular velocity
corresponds to a mean harmonic height.
156 THE VELOCITY OF SPORADIC METEORS—II IX, §1
considered that the use of mean heights, instead of individual heights,
was justified. In this way many meteors observed in the rocking mirror,
but without measured heights, could be included in the analysis of linear
velocities.
The theoretical values of the angular velocity w of these meteors were
computed from
__ „ SUIT) cos z , .
w = 57-3v--deg./sec., (1)
h
where rj is the angular distance of the centre of the trail from its radiant
and z the zenith distance of the trail. This value was compared with the
measured rocking-mirror value w n . The errors in angular velocity were
of a logarithmic character with the average \og(wJxv) = 1-067±0-035.
No systematic dependence of this ratio on duration, length of trail, or
angular velocity could be found. Opik concluded that w D did not involve
any large systematic error and that the constant systematic error
probably consisted of an overestimate of the angular velocity by about
7 per cent. The errors in the individual observations he considered to
be due to errors in the length of the trail as traced on a star map. The
durations were thought to be very accurate, the error amounting to no
more than x Jq sec. for short durations (< 0-4 sec.).
Opik applied this systematic correction in the ratio 1:1-067 for w Q to
investigate the corrections of w x relative to w n . The resultant corrections
necessary to w x are given in Table 32.
Table 32
Corrections required to Angular Velocities w l in the Rocking-mirror
Observations
u>, observed
(deg./sec.)
120
16*0
20*0
24*0
44*0
60*0
720
it, corrected
(deg./eec.)
1
11-6
15-9
20*4
25*3
29*8
490
65*0
76*2
Assuming uniform accuracy for w n the relative weights of Table 33 were
derived from the internal agreement of w n and w v
Table 33
Relative Weights to be assessed to Angular Velocities observed in Rocking
Mirror
Method and angular velocity .
w x < 17-9
t v x = 180-23*9
xo x > 24 0
Relative weight
U
0*5
0*8
10
IX, §1
THE WORK OF OPIK
By applying Tables 32 and 33 to the observed angular velocities the
final weighted mean angular velocity w was obtained.
In the subsequent computation of linear velocities, average heights
of the trail centre were assumed to be a function of the zenithal angular
velocity — wsecz. (2)
The relation between h and w t was obtained from the data in Table 34.
Table 34
Relation between Height and Zenithal Angular Velocity
u) t deg./sec. .
No. of heights
Harmonic mean h, km.t.
0-19 9
34
780
200-39-9
53
81-8
400-79-9
35
86-8
> 80-0
12
83-7
All
134
82-4
Probable orror, km.
±1-5
±1-3
±1-8
±2-8
±0-8
Smoothed relation finally adopted
h .
B
10
77-9
20
796
30
82-0
40
83-8
60
84-9
60
85-8
70
86-2
B
The linear velocity was then computed from
u>h secz
v =
57-3
(3)
In both (1) and (2) the curvature of the earth is neglected. Opik’s
justification is that errors thereby introduced tend to cancel in the mean,
and in any case the average error produced by neglecting the curvature
is only 2-3 per cent, with a spread of ± 1-7 per cent, for the actual region
of observation.
The spread in log|- ^ b3 -j for the 64 radiant meteors was ±0-165
(standard deviation). Correcting for an assumed 7 stray meteors gave
±0-157. This gives for the empirical value of the observational probable
error in log w a figure of ±0-106, or ±25 per cent., which is larger than
would have been expected from the internal agreement of w D and w v
The velocities were finally corrected for the earth’s orbital motion
graphically to give the heliocentric velocity V 0 . An example of the final
data produced in this manner is shown in Table 35, these being the data
given by Opikf for 1931 November 14.
f The arithmetical mean of all the heights was 85-0 km. These are relative to Flag¬
staff, Arizona; reduction to sea-level requires a correction of +2-1 km.
x Opik, E. J., Circ. Harv. Coll. Obs., loc. cit.
Table 35
Example of Final Data produced by Opik from the Rocking-mirror Observations
158
THE VELOCITY OF SPORADIC METEORS—H IX, §1
O'?
O £
o
rt«n-nciP3nnM--<e)M
pii
^ 2 © 13 ,ON W C . f CO
«- ®» : 13 ;o®«© : ;® f
•S < fr,
h>
||I
ili
CJO'fOOMNCC-l'Nei'tO
It
ovonfier>(ooMv-co®
ti n :i cj n ci n :i n :i - ei - -
'5 S
1*1
Oh«0«®N©o-ONO®
^ — — --H-cinNcin
j 1
a S S a 8 8 8 5 5 S S 2 2 2
©© — © — ©©©©©©©©©
||
I*
«on®eoo«npio®MO
N«oh«eo-vo®fov
— — — — — C4 — — — —
III
sn»on®ci®-tnv®o»
o«o®®e»«ho»o®o
S«00-f®«a0ffflM3®
©f — »3®t^f©« — ClOOf
?t e*j — — n — « —
||
II
owsoccooooocoaoooo
« — owffeoffwrtffw
|I
3 2
oexf — cceccc — ®e v - f
otbti-ono-i'cevvi'n
neovo — — ooaoao® — —
n n n n — — —
60 !
159
IX §2 THE WORK OF OPIK
2. The Arizona results of Opik and Boothroyd
Although a very large number of velocities were measured during the
Arizona expedition, those measured by Opikf (naked eye) and by Booth-
roydj (telescopic) represent data obtained by experienced observers.
They were therefore considered by Opik§ to be worthy of separate treat¬
ment. The adaptation of Opik’s technique to the telescopic observations
has been described in Chapter II. The data treated by Opik§ consisted
of 279 naked-eye observations made by himself and of 580 telescopic
observations!! made by Boothroyd.J
The lists of observations (for example Table 35) give the observed
distribution of projected heliocentric velocities. From these Opik
attempted to deduce the true distribution of heliocentric velocities in
space in two steps, (i) The observed distribution was freed from the
effects of accidental errors of observation to obtain the true distribution
of projected heliocentric velocities, (ii) By making plausible assumptions
about the distribution of angles between the velocity vectors and the
line of sight, the probable distribution of heliocentric space velocities
was obtained.
(i) As discussed in § 1 above, the observational error in the angular
velocities had a logarithmic character. For a constant relative accuracy
in the observed angular velocity, the relative error in the helio¬
centric velocity V 0 depends upon the direction (for directions from the
apex the relative error will be larger than average; for directions from
the antapex, smaller than average). By comparison with meteors from
known radiants the probable error in the linear velocity was found
to bo ±0106 in log v. Assuming this constant relative error in the
observed velocity, the probable error in the transverse heliocentric
velocity V 0 (that is at right angles to the line of sight) was calculated
graphically for each case. Further detailed treatment gave the frequency
of errors for different limits of V 0 , and enabled a table to be constructed
showing the complicated law of observational errors in V 0 . With the aid
of these data the true distribution of the projected heliocentric velocities
was calculated by a method of successive approximations.
(ii) In order to find the distribution of space velocities from these data
it is necessary to know the frequency of the ratio
f Opik, E. J., Circ. Harv. Coll. Obs., loc. cit.
x Boothroyd, S. L. f ibid. (1934), no. 390. § Opik. E. J., ibid. (1934), no. 391.
|| These aro about five-sixths of the data given by Boothroyd (loc. cit.). Opik rejects
Boothroyd’s observations of durations < 0027 sec., owing to the uncertainty of tho data.
160
THE VELOCITY OF SPORADIC METEORS—II IX, §2
where V 0 is the projected velocity, and V h the heliocentric space velocity.
Since x was continuous, Opik calculated the frequency of x for two cases,
(i) for a random distribution of directions, (ii) for a spherical surface
density of radiants proportional to cos^ (z being the zenith distance of
the radiant). The distribution of a; is rather similar in both cases.
Actually Opik gave reasons for taking the cos^ distribution for V h > 42
km./sec. and the random distribution for V h < 42 km./sec.
Opik s solutions for his 279 naked-eye observations are given in
Tables 36 and 37.
Table 36
Distribution of Heliocentric Space Velocities \ of 279 Naked-eye
Observations
V b km./eec.
Number
Percentage
Uncorrected
Corrected^
36
32
7
2-6
42
39
76
27-3
60
47
62
18-7
60
67
47
16-8
72
69
26
9-3
86
83
16
6-7
101
98
12
4-3
120
116
16
6-4
143
139
16
6-7
170
166
10
36
202
197
2
0-7
All
279
1000
f The uncorrocted values of V h are here corrected for (i) tho earth’s gravitational
attraction, (ii) an estimated average constant correction of -2-6 por cent, to allow for
the possible ellipticity of the stream meteor orbits which were used in standardizing the
data. Tho gravitational correction was calculated by averaging three cases: (a) direc¬
tion from apex, weight one, (6) direction from antapex, weight one, (c) radial heliocentric
direction, weight four, giving the following values:
km./sec.
Correction km./sec.
28
-36
30
-3 3
34
-2-9
38
-2-6
42
-2-1
60
-16
60
-M
100
-0*7
140
-0-5
200
-0-3
IX, §2
THE WORK OF OPIK
161
Table 37
Distribution of Projected Heliocentric Velocities V 0 of 279 Naked-eye
Observations
V 0 km./sec.
uncorrected
Number
Observed unsmoothed
Observed
smoothed,
all magni¬
tudes
True,
corrected for
accidental
errors
Computed from
distribution of
V h (Table 36)
m < 3-7
m > 3-7
All magni¬
tudes
< 14-9
10
3
13
13 0
10-7
11-7
150-17-8
3
1
4
36
M
4-9
17-9-2 M
8
8
5-4
3-5
7-4
21-2-25-1
5
2
7
8-4
6-5
10-7
25-2-29-9
12
1
13
15-7
4-7
163
30-0-35-7
28
8
36
34-9
33-8
28-5
35-8-42-3
36
12
48
480
71-5
59-4
42-4-50-3
27
15
42
39-0
49-6
42-4
60-4-59-9
16
9
25
28-5
29-9
30-0
60-0-71-5
12
11
23
21-3
18-6
18-4
71-6-84-7
10
7
17
162
12-7
12-8
84-8-100
4
7
11
13-0
10-6
10-8
101-119
8
3
11
11-0
no
109
120-143
6
5
11
8-5
9-0
9-1
144—169
2
1
3
5-5
4-7
4-8
170-201
2
1
3
1-1
0-9
> 201
2
2
4
mm
0-0
0-0
All
191
88
279
279-0
279-0
279-0
Table 38
Distribution of Heliocentric Space Velocities V h for 580 Telescopic
Observations
Vt, km/sec.
Average magnitude = 6-5
Average magnitude *=8-5
Uncorrected
Corrected f
Number
Percentage
Number
Percentage
30
27
0
0
14
4-1
36
33
77
32-1
11
3-2
42
40
32
13 3
0
0
50
48
0
0
0
0
60
59
0
0
19
5-6
72
71
16
6 7
23
6-8
85
84
36
15-0
28
8-2
101
100
38
15-8
10
2-9
120
120
30
12-5
0
0
143
143
10
4-2
192
56-6
170
0
43
12-6
202
0
0
239
1
04
0
0
All
240
1000
340
100-0
t Correction only for earth's gravitational attraction.
3595.68
M
Table 39
Distribution of Projected Heliocentric Velocities V 0 for 580 Telescopic Observations
162
THE VELOCITY OF SPORADIC METEORS—II
IX, §2
103
JX §2 THE WORK OF OPIK
Opik treated the 580 telescopic observations of Boothroyd in a similar
manner. In this case no standardization with shower meteors was
possible because of lack of knowledge of radiants and individual heights.
An average height for aU meteors was therefore assumed. The probable
error in Boothroyd’s log w 0 was found to be ±0 065 corresponding to a
relative probable error of ±11 per cent. The solution for the helio¬
centric space velocities was made in a similar manner as for the naked-
eye observations. The results, corresponding to Tables 36 and 37 for
the naked-eye data, are given in Tables 38 and 39.
Although these results are inadequate for a discussion of small
differences in heliocentric velocity, such as would be necessary to dis¬
tinguish between parabolic and highly eccentric elliptical orbits, the
data show the existence of an appreciable number of high hyperbolic
velocities and the fact that the percentage increases with decreasing
brightness. Opik gives the data in Table 40 for the percentage of helio¬
centric velocities exceeding 62 km./sec. for different magnitudes.
Table 40
Percentage o} Heliocentric Velocities exceeding 62 km./sec. according
to the preliminary rocking-mirror results
Magnitude . . • • • 1
2-5
4 5
6-5
8-5
Percentage of high-velocity meteors .
20
45
56
87
Furthermore in the period October to November 1931, covered by
the naked-eye observations, Opik concluded that all the sporadic
meteors possessed hyperbolic velocities and were therefore of extra¬
solar origin.
3. Preliminary treatment of the complete Arizona velocity
measurements
The naked-eye data on 279 meteors discussed above were obtained
from the personal observations of Opik in Arizona during October and
November 1931. After Opik’s departure the observations were continued
by R. Wilson and D. Hargrave until the end of the expedition. From
the combined observations a total of 1,436 meteor velocities was obtained
(611 by R. W., 546 by D. H., 279 by E. O.). A lengthy and comprehensive
analysis of these data has been made by Opik.f The method of reduction
was essentially the same as that described above. Meteors belonging
t Opik, E. J., Publ. Tartu Obs. 30 (1940), no. 5. A short account is given in Opik,
E. J., Mon. Not. Roy. Aetr. Soc. 100 (1940), 315.
164 THE VELOCITY OF SPORADIC METEORS—II IX, §3
to showers where a parabolic velocity could be assumed were used to
determine the systematic errors of the observers. The standard deviation
in log w for the shower meteors was found to be ±0-165 (D. H.); ±0-176
(R. W.); ±0-165 (E. 0). Including the error dispersion in the assumed
mean height the observational probable error in logw was taken as
±0-106, the same as previously. The number of shower meteors used in
this standardization was small—69 for E. O., 41 for R. W., 32 for D. H.,
from which 5, 6, and 11 were rejected respectively. Opik justifies this
rejection on the grounds that these represent a peculiar selection of
stray meteors.
The correlation between height and angular velocity was obtained
from 486 cases observed by R. W. and D. H., in which both height and
velocity were measured. The relation adopted is given in Table 41, which
is to be compared with Table 34 for the earlier analysis, from which it
differs somewhat.
Table 41
Relation between w z and h for 486 Observations in the complete
Arizona Data
(Jog./HOC. .
m
16
20
24
28
32
>36
h km. .
BO
880
89-7
91-2
92-4
92-8
930
The linear velocity at right angles to the line of sight was then calcu¬
lated as described above.
The Arizona records showed that the results of R. W. yielded 20 per
cent, velocities, D. H. 19-6 per cent., and E. 0. 66-7 per cent. In view
of these differences Opik gives attention to the question of selection of
the data, with respect to angular velocity, magnitude, position in the
field of observation, length of trail, and direction of motion. Although,
from an analysis of the data, Opik found marked selection effects relative
to these variables, there were also various equalizing factors which led
him to conclude that the uncorrected velocity list must represent fairly
well the distribution of intermediate w , with a deficiency in very large
and very small w. He decided to use the statistical data, uncorrected for
selection, because a satisfactory determination of all the selection factors
was not possible on the basis of the existing data.
Following the same law of observational error dispersion in V 0 . and
of the relative frequency of projection ratios V 0 /V h (p. 159), Opik gives
the provisional distribution of heliocentric space velocities as shown in
165
IX §3 THE WORK OF OPIK
Table 42 for the three observers. This is to be compared directlyt with
the distribution given in Table 36 for the 279 measurements of Opik
which are also included in Table 42.
Table 42
Provisional Distribution of Heliocentric Space Velocities for the 1,436
Arizona Velocities (all directions)
V h km./sec.
E. 0.
(number)
R. W.
(number)
D. U.
(number)
All observers
(number)
< 15
0
0
23
23
18
0
0
0
0
21
0
0
2
2
25
0
0
3
3
30
0
0
3
3
36
7
84
34
125
42
76
173
64
313
60
52
125
113
290
60
47
102
164
313
72
26
101
77
204
85
16
25
61
102
101
12
0
0
12
120
15
0
0
16
143
16
0
0
16
170
10
0
0
10
202
2
1
0
3
240
0
0
2
2
All
279
611
546
1,436
4. Detailed treatment of the complete Arizona velocity measure¬
ments
Although the individual differences in the results of the three Arizona
observers were considerable Table 42 indicates that the statistical data
are not radically different. Opik therefore joined together the data of all
three observers, which then provided sufficient material for a detailed
analysis of the different directions of motion. Following Opikf we shall
first outline his method of correction for observational error dispersion,
the results of which have already been presumed in deriving Tables 36
and 42 (§ 2 (i), p. 159, and § 3, p. 164). Secondly, his more precise
method for finding the distribution of space velocities will be described.
This supersedes the elementary treatment described in § 2 (ii) used in
the computation of Tables 36 and 42.
t The values of V h in Table 42 are not corrected for the earth’s gravitational attrac¬
tion or for tho effect of the ellipticity of the shower meteors on the standardization of
the velocity scales.
\ Opik, E. J., Publ. Tartu Obs. 30 (1940), no. 5, p. 27.
166
IX, §4
THE VELOCITY OF SPORADIC METEORS—II
(a) 6pile'8 Corrections far Observational Error Dispersion
The correction made by Opik for observational errors is of primary
importance in his analysis. In this section an outline of the treatment
will be given, with an example of its influence on the observational
results.
Let x = true quantity,
F(x) dx = frequency of x,
y = observational error,
x(y> x ) dy = frequency of y,
f = x+y = observed quantity,
$({) df = observed frequency between £ and £+d£.
Then the integral equation of diffusion is
+®
i’(f) = J F(f-y)x(y.f-y) dy. ( 4 )
— 00
When 0 and \ are known, the true distribution is determined by (4).
An analytical solution for the case of a Gaussian * = *(y) has been
given by Eddingtont but even in this case the method cannot be used
for a large error dispersion. Opik used a method of successive approxima¬
tion. With = j dy the first approximation to F is
Fi = <D+(<D-<Dj) = 2<D-<D l .
With $2 = / FjX dy the second approximation is
F 2 = <D+(F x —0> 2 ),
and so on. The numerical procedure is actually a direct calculation of
(Fj—<I> 2 ) instead of <b 2 . Generally one to three approximations lead to
a good solution, which is checked by substitution in (4).
The dispersions A (mean square deviations from the arithmetical
mean) satisfy ^ = (6)
This is true when £ is a directly measured quantity, and \ is the error
function representing the distribution of y = (£—x) for a given value of
x. But if the observed quantity rj is a statistical average value of x,
corresponding to a certain observed criterion £' (Opik cites as example
f Eddington, A. S., ATon. Not. Roy. Astr. Soc. 73 (1913), 369.
IX, §4
spectroscopic
THE WORK OF OPIK
absolute magnitudes), t) = *(£')» then
to
F(x)= J ^(x-y)x.(y.*-y)dy,
— to
A? = AS+AJ,
where x = yj+y,
0 (yj) dtj = observed frequency of r\,
v , v dY = apparent error function determining the distribu-
Xl(y '^ tion of x—n = x—x(£').
Thus the first case involves a subtraction of the error dispersion (eq. 5)
and the second case an addition (eq. 7).
In the present observations x = log v and x is assumed to be Gaussian
depending on the error alone x = x(Y>- Also we have seen that the
probable error in log v = ±0-106. The solution was then made according
to (4). Table 43 gives the distribution of the geocentric tangential
velocity v for all three observers together, for different values of P,
the direction of motion with respect to the apex (P - 180 is from t e
apex- P = 270° is towards the sun and downwards). For each P, the
first column gives the smoothed observed value of v, and the second
column the value of v corrected for the error dispersion as above, lhe
roman figures at the head of this column give the order of the final
approximation in F adopted.
(b) Opik's Calculation of the Distribution of Space Velocities
The approximations described in § 2 (ii) were used by Opik in the
preliminary treatment to derive the distribution of space velocities
given in Tables 36 and 42. His exact treatment for the complete Arizona
data is described in this section.
(i) The frequency of the projection ratios. In order to find the dis¬
tribution of space velocities from the data in Table 43 it is necessary
to know the frequency of the projection ratios sin r, for each ‘ P-sector’,
yj being the angle between the line of sight and the trajectory of the
meteor (or the angular distance of the centre of the trail from its radiant).
Certain assumptions are still made in order to simplify the analysis:
( 1 ) the whole area of observation is replaced by a point at its centre
45° N. of the zenith (8 = +90°); ( 2 ) in each P sector a homogeneous
distribution of P is assumed, dn/dP = constant, of a density corre¬
sponding to the median value of P.
Table 43
The Distribution of Geocentric Tangential Velocities v and the Correction for Error Dispersion
168
THE VELOCITY OF SPORADIC METEORS—II ix, §4
0
<0
3
u
oooocoo^o^vaoco-t^-,0^00
oo©©«oc^,oeooieic»c».i-6©66©©©
0
■*»<
i
O
°oo-voiovP 5 e< 5 fficici-- 6666 ooo
0
*0
*-«
CO
Is
SAA? ? °^"”®®" a0l °00-0
ooow^^o > - a} ^ lOK3e ^ c ^^ 6<i)66oocj
ci
c-
M
t®
•>
§
??®r l r?®«rN--oo»oiant )
o-.-.co^w t » COC o^»« 4 cb«^ 666 000
0
VO
CD
CJ
Is
Nvovno® evo -tcn®oiQciooci
00! ” ,, '2asssss:s:»^ 0 <= = 0
O
y*
a
1
to
•a
M
IS
co
ci
CO
S 2 - 25 SESSSSs a g S SS 2 gggg
CO
0
CO
0
VO
w
Cl
I s *
AAA22® <? T , ® < ? e ?«?* , '««OOOOM«o«o
° 000 o°*::;s 5 ssr»»
Cl
1
AAAA®' r ‘ ? ”^ < ? e P‘? C ?‘ 0<N ‘ 0 '» , ©«>CI©ao
°oo = -'-2;oj ls , S o : „i,.._ 6
—
—
Cl
to
Cl
i*
oooooc,,o 2 = o s; „«„.^. 6
o>
Cl
OO« 9 « r c ? r r , o c poOO ^00 00 t- U 500 t )® tC ,<»
©
—
Cl
0
s
—
SSAAAAA®®^ e i ,< ?^? 00,0 OOOnN
ooooooo-n-,..„„on66666
s
—
??o?'?'?-?'?o?oo«» V oi'h (0 «n
s
—
0
3
is
????®Nn« < ei r ttn,, XBl0O oooo
oooooNn»e®tt«h«tb»n6666o
1
ooo--Nn , ooh« a i h#l ovn-6666
h
0
2
is
^ , ”^? 7 ?®f | Ni 0 -fOht»®OOO
ooooo-.w-»o^ w «c<-6666oooo
O
CO
|
coco-toatovorjccr-coo-TcccocoiMO
©oooo-cieoeoebeocic*--©©©©©©,^
3
0
I 5
VO
—
•
•j
£
®r^®cctDtO'Kcnr«r*®tawco
00066666AAA-AA60000000
»o
—
0
1-
00000000 — — — weoiboooooooo
. •
.2
0
fliaooooot.-n^.p.Hoooo
00000000 — — — cifinfiooooooo
®
—
0
O
- 1
n -
IS
oooiooMhCf.t.cuo^iaciooo
0
CO
11
ft.
i
0
-naoo 9 ci? , -ociccionoh V ci
ooo-?i(i nn „ N NH---666oooo
0
CO
V
>4 ,
1 ;
lfl '?®*rr® , r nn ®
txi ,l,| *- , oo««i 6 ffl- 4 o on 2 -®
• r i°'T *T *7 w « w 0 ^ 0 « h » - — -O' <o © eo ©
j.^<i-2 2^«S§«?!SSSS222^§A
4.1
> *i
rl
ix, S*
169
THE WORK OF OPIK
If B is the density of radiants per unit solid angle at vertical incidence
and £ the angular distance from the apex, then Opik has shownf that
the surface density of radiants f(£, r,) can be written as
= B(cosz)\
where z is the zenith distance of the radiant, (fc = 1 would correspond
to a case in which all meteors were sufficiently massive to be observed,
or in which the apparent brightness did not depend upon the angle of
incidence; k = 2 corresponds to brightness varying as cos z and with the
numbers of meteors increasing by a factor of 2-5 per magnitude.)
Table 44
Stream Intensity nJC {for rj = 0° to rj = v ) for k = 1,
B = 1 at z = 45°N.
A
wrm
30°
C3
mm
120 °
150°
180°
V
isa
330°
300°
240°
210 °
(down)
dtg.
JJH
mu
PU
0
HaJ
0-000
0-000
0-000
10
0027
0027
0028
ram
0-032
0-033
0-033
20
0-090
0094
0-104
0 117
0-130
0-140
30
0-159
0-171
0-250
0-296
0-329
0-341
40
0-207
0235
dj
0 413
0-516
0-591
0-619
45
0-215
0 0
• •
0 0
0 0
0 0
• •
49-1
• •
0-258
0 0
• •
• •
• •
0 0
50
• •
0 0
0396
0-587
0-778
0-917
0968
60
• •
0 0
0443
0-750
1-057
1-282
1-364
63-4
• •
0 •
0-466
• •
• •
• •
0 0
Q.
• •
0 0
0 0
0-883
1-334
1-663
1-784
Ki
• #
0 0
• •
0-970
1-582
2-031
2-195
90
0 •
0 0
0 0
E£ZvJ
1-786
2-360
2-571
100
0 0
0 0
• 0
• •
1-928
2-629
2-886
110
0 0
0 0
0 0
0 0
2-005
2-826
3-126
116 6
• 0
0 0
• 0
• *
2-016
# •
• «
120
0 0
• •
0 0
0 0
0 0
2-940
3-278
130
0 0
0 0
0 0
0 •
2-978
3-348
130-9
0 0
• 0
0 0
0 •
2-980
. •
135
0 0
• •
3-356
In the present analysis we use A as the direction of the meteor with
respect to horizontal coordinates! (A = 0° denotes motion vertically
t Opik, E. J., Ann. Harv. Colt. Obs. 105 (1937), 568.
X A = P— 90°+ t, where t is the mean local time.
170
THE VELOCITY OF SPORADIC METEORS—II
IX, §4
up in the northern hemisphere), then putting A = e and B = 1
^5 = sm 2 Tj—(rj—sm-qcosT])cos A (for k = 1), (8)
_ —sm 2 A{l — cos 3 tj)+V2cosM(1—costj) — ^cos Asin 3 ^
(for fe = 2), (9)
where C = (V2/4) d A. These expressions give the integral number of
radiants n,, from rj = 0 to tj, within the directions A to (A+dA).
From (8) and (9) Tables 44 and 45 respectively can be calculated,
giving the relation between n^/C and A for k = 1 and k = 2.
Table 45
Stream Intensity n^/C (/or rj = 0° to rj = rj) for k = 2,
B = 1 at z = 45° N.
A
0 °
30°
60°
90°
120 °
150°
180°
V
(up)
330°
300°
270°
240°
210 °
(down)
dtg.
0
0 000
0 000
0 000
0 000
0-000
0 000
0-000
10
0016
0017
0019
0 021
0023
0-025
0-026
20
0047
0-051
0-062
0080
0-100
0-117
0-123
30
0071
0-081
0-112
0-165
0-230
0-285
0-307
40
0080
0-096
0-152
0-260
0-402
0-530
0-582
45
0080
• •
0 0
0 0
• •
0 0
0 •
49-1
• s
0099
0 0
0 0
0 0
0 0
0 0
50
• •
• •
0-175
0-346
0-597
0-830
0-928
60
• •
# 0
0-182
0-412
0-792
1-161
1-319
63 4
• •
0 0
0-182
• 0
. ■
0 0
• •
70
• •
0 0
..
0452
0-963
1-487
1-712
80
• •
0 0
• •
0469
1-094
1-772
2-068
90
• •
0 0
..
0-471
1-179
1-993
2-357
100
• •
0 0
0 0
0 •
1-222
2-142
2-560
110
—
• •
0 0
0 0
• •
1-235
2-223
2-697
1166
• •
• 0
0 0
• a
1-235
0 0
0 0
120
• •
0 0
0 0
..
0 •
2-251
2-733
130
— —
• •
0 •
0 0
..
0 •
2-266
2-746
130-9
• •
0 •
0 0
■.
0 •
2-257
0 0
135
• •
1 "
0 0
••
0 •
0 0
2-748
As regards the actual value of k to be taken in the reduction (jpik
represents the law between k = 1 and k = 2 by linear interpolation:
(cosz)* = pcosz+(l-P)cos*z (10)
(where for k = 1, (S = 1; for k = 2, P = 0).
171
IX §4 THE WORK OF OPIK
During the entire Arizona expedition the observed meteor streaming
near the meridian was as follows:
Meteors moving up
Meteors moving dot
L*n
Ratio
doum/up
A
Number
$
A
Number
s
--
l 0°-29 o
1431
I 150-179
3.266 \
+ 14°
20 - 0/1
N. of zonith
(330-359
HI)
+ 76
l 180-209
2,419/
■
f 150-179
138 \
« .o
I 0-29
1,935 \
+ 56°
13-4/1
S. of zonith
( 180-209
108/
—
( 330-359
1,369/
S is the mean declination for the given sector estimated on the basis
of Tables 44 and 45 with p = 0-5. Opik considers the inequality in the
N/S ratios to be an effect of declination which he represents by an
additional factor b co8 * s in (10). For the limits of A the theoretical ratio
down/up is = 13-4 for fe = 1 (Table 44), and - = 27 8 for
k = 2 (Table 45). With these and the observed ratios (10) gives
P = 0-54±0-045; b = 1-374.
In the subsequent analysis Opik takes p = 0-5 (actually the sum of
Tables 44 and 45 was used, which corresponds to 2n^/C).
As regards the increase in the apparent density of radiants tow-ards
the apex Opik shows that the distribution can be represented satisfac¬
torily by the expression
B(cj) = a C08<t x const., (11)
where e, is the distance of the apparent radiant from the apex. From
the relative frequency of velocities in the region P = 165°-j-195°,
compared with P = 15°-f 345° (Table 43) and with the value of b
found above, Opik evolves the working formula
B' = a cos c * b 008 * 5, (12)
with a = 2-77, b = 1-374, for the apparent density of radiants (vertical
incidence).
Tables 44 and 45 are arranged according to the angle A , whereas the
statistics (Table 43) refer to the apex direction P. For the centre of the
observational area these angles are connected by A = (P—90°-f-t),
where t is the mean local time. Hence, for a given P sector, different A
sectors contribute during the night. The theoretical distribution for a
given P sector is computed by weighting the data of Tables 44 and 45
according to the observational times. For the calculation of B' in (12)
172 THE VELOCITY OF SPORADIC METEORS—II IX, §4
it is assumed that 8 apex = 0 and for a point (S x , P) that
cos €j = — cosSjCOsP. (13)
The original coordinates are tj, P. The declination varies slightly with
A. The average declination for given ( 77 , P) is found, weighting the data
according to the observational times as above. B' is then calculated
using (12) and (13). A selection of the final theoretical distributions is
given in Table 46. (The original contains the distribution for P in 30°
intervals from P = 15° to 345°.) The three columns of this table give
the following data for the limits rj 1 and tj 2 , and for A P = 1 (one radian),
corresponding to a solid angle S = cos co 8 tj 2 :
(i) N z , the intensity of streaming for B' = 1 (uniform distribution of
directions),
N z = 4V2 I (cosz-f cos^sinrj d 77 ,
i?*
found by summation of Tables 44 and 45 and by taking the corresponding
differences between rj l and rj 2 ;
(ii) the provisional radiant density B', computed by using (12);
(iii) the final intensity of radiation corresponding to B',
N v = B'N Z .
Table 46
Calculated Stream Intensity
(Northern Region, Arizona)
V
P - 46°
P - 135*
P - 225*
P - 316°
A.
B'
A’n
E9
□
An
B'
A*n
n
B'
An
0°
10
20
30
40
60
60
70
80
90
100
110
120
130
136
0046
0 120
0 152
0 162
0124
0098
0072
0051
0029
0013
0006
0002
0 000
0 000
1 000
0-893
0813
0-757
0-720
0 698
0-678
0-676
0-673
0-668
0 673
0-675
• •
0046
0 107
0 123
0-115
0-089
0068
0049
0 034
0020
0-009
0-004
0 001
0 000
0-000
0046
0-118
0-144
0-144
0 113
0084
0062
0 041
0 024
0010
0 004
0 001
0-000
0-000
1-000
1140
1-324
1-545
1- 799
209
2- 38
2-59
2-73
2-82
2-73
2-59
0046
0 134
0-191
0223
0203
0-175
0-147
0-106
0065
0028
0 011
0 003
0000
0 000
n
1-140
1-325
1-545
1- 799
2- 089
238
2-69
2-73
2-82
2-73
2-59
2-38
2-09
1-94
0062
0-237
0-465
0-734
1-006
1-220
1-300
1-204
1-015
0716
0-445
0-181
0-071
0-006
0055
0 180
0310
0420
0-500
0533
0-527
0-468
0-383
0-278
0-183
0087
0-029
0-003
0-893
0 813
0-767
0-719
0-698
0-678
0-676
0-673
0-668
0-673
0-676
0-678
0-698
0-708
0-049
0-146
0-236
0-301
0-349
0-361
0-355
0314
0-265
0-187
0-123
0-059
0-020
0-002
Sum
0-865
• •
0-665
0-791
m
1-332
3-791
••
8-662
3-966
••
2-766
. r
<i = i
, = 34°-9;
«= +60°;
1 l’;z = 72°-9
Vff = 43°-5;
$, = +53**;
«, = 65°; £ = 80 8 -3
= 64°-7;
S, = +20°
(, = 48° ;z = 4 8°-3
Vtn = 58°-3;
g,= +27*;
i, = 129° ;i = 38°-7
173
IX §4 THE WORK OF OPIK
If B is the true mean density of apparent radiants, the observable
probable number of meteors originating from the sector P to P+ A
and from a distance to rj 2 is
with A P in radians.
For the 30° sector width considered here this becomes
n
^ - 10-80'
By using this formula the relative figures in Table 46 can bo converted
into absolute ones for the specific value A P = 30°. At the foot of Table
46 the coordinates of the effective point of radiation are given. ^ off is the
value of t) which halves £ N,; t v i v and z refer to the point (P,W-
Opik compares the observed distribution of velocities according to
P with the theoretical distribution determined by the sum of N v and
shows that the degree of approximation in Table 46 is reasonable. There
are systematic trends for different P in the ratio observed/calculated
within the limits 0-68 to 1-54. Opik considers this to be reasonable since
the error in the distribution of sin q inside a given P sector, which is
required, must be smaller by an order of magnitude than the errors in
the absolute frequencies for different P sectors. Finally the distribution
of the projection ratios, sin q, is given in Table 47 for cases of B = const.,
and B' defined by (12). (Table 47 is a selection of the original correspond¬
ing to the P values in Table 46.) The similarity of the two solutions
leads Opik to conclude that no further approximation is required and
the results in Table 47 for B' defined by (12) are used in the subsequent
analysis.
(ii) The distribution of space velocities. From the above data Opik
determines the distribution of space velocities by employing equa¬
tion (4), used in calculating the error dispersion. In this case x is the
frequency function of projection ratios given by Table 47, <1> the frequency
of tangential velocities corrected for error dispersion (Table 43), and F
the frequency function of space velocities which is required. Successive
approximations are not required and the numerical solution proceeds
as follows:
The discrete values of the space velocity v are spaced in the ratio
*J2/1 as for v in Table 43 and sin q in Table 47. Let V! be the highest
value of v and let the number between v x and v 2 = Vj/^/2 be n, (Table
43 corrected). Let the frequency of projection ratios from 1-000 to
174
THE VELOCITY OF SPORADIC METEORS—II
IX, §4
Table 47
Relative Frequency of Projection Ratios (sin -q)
Case (a): B = const.; case (6): B' defined by formula (12). Case (6) is adoptod in
the solution for space velocities.
P =
45°
P =
135°
P =
225°
P =
315°
sin i j
(a)
(6)
(a)
(6)
(a)
(6)
(a)
(6)
1000
0-842
0-707
0-594
0500
0-421
0354
0-297
0-250
0-210
0-177
0-148
0-125
0-105
0-000
0-228
0-202
0206
0-303
0-516
0-598
0-523
0-503
0157
0-131
0144
0 123
0-161
0 133
0-175
0-131
0-173
0-100
0-170
0087
0-170
0-099
0-168
0-100
0-116
0116
0 121
0-112
0-072
0-056
0-071
0-073
0-090
0102
0094
0079
0-044
0-030
0-043
0047
0-073
0-072
0-076
0056
0-030
0-021
0-030
0-033
0-060
0-063
0057
0041
0-020
0-012
0-019
0-022
0042
0048
0043
0-031
0-014
0 008
0-014
0-016
0-031
0033
0-033
0021
0010
0-006
0-010
0-011
0-021
0-026
0-026
0-015
0007
0-004
0-007
0-008
0-015
0021
0-018
0-011
0-004
0003
0-004
0-005
0010
0015
0-012
0-008
0-003
0 002
0-003
0-004
0-007
0-011
0009
0005
0 002
0-001
0-002
0-003
0019
0-024
0 021
0012
0-005
0-002
0-005
0-007
Sum
Mean
1-000
1-000
1-000
1-000
1 000
1-000
1-000
1-000
8 in r)
0-696
0-570
0-583
0655
0-775
0-819
0-777
0-764
0-842 be xo (Table 47); the frequency of space velocities Vj = v x is
N, = nJxo : this number is then multiplied consecutively by the
fractions x fr° m Table 47 and the products subtracted from the
corresponding v frequencies. A new distribution of v is obtained with
v 2 the highest value, and with n 2 between v 2 and v 3 . The frequency of
space velocities v 2 = v 2 is then N 2 = nJxo an ^ 80 on - A selection of the
distribution of space velocities for the same P values as in Tables 46 and
47 determined by this method is given in Table 48. The various
columns in Table 48 are as follows:
1. v = the discrete values of the space velocities corrected for
the ellipticity of the standard shower meteors.
2. v = 125) the geocentric velocity corrected for the attrac¬
tion of the earth.
3. € V 8, = the apparent distance from the apex, and the declination
of the centre of radiation of the P sector.
4. V = mean heliocentric velocity corresponding to the centre of
radiation.
6. c, 8 = the true or heliocentric distance from the apex and the
declination of the centre of radiation.
176
IX. §4
THE WORK OF OPIK
In standardizing the velocity scales Opik assumed that the shower
meteors were moving at the parabolic velocity limit. In deriving Table
48 he introduces a tentative correction of 0-986 based on the velocities
then believed to apply for the Lyrids, ,,-Aquarids Perse,ds, and Leoruds^
(i m The distribution of heliocentric velocities. Opik derived correction
factors for the above data to allow for the gravitational attraction
and orbital velocity of the earth, and after transforming from geocentric
to heliocentric coordinates presented the final data given in Table 49.
The table is arranged according to the observed direction of motion P,
and for different limits of the heliocentric velocity V it gives: e the dis¬
tance from the apex and 8 the declination of the true (heliocentric)
centres of radiation; n the number of observed meteors; v the mean
velocity of impact on the atmosphere upon which the luminosity of a
given moss depends.
Table 48
Distribution of Space Velocities
P
P
n
1
».
km./eec.
<
s
n
km./tcc.
«
s
V
km. 1/tec.
V
km./eec.
P
- 45“
P =
135°
deg.
deg.
deg.
deg.
deg.
+
deg.
+
deg.
+
deg.
_ +
OOI
281
0
Ill
60
293
116
56
0
65
53
270
71
56
•ol
235
0
111
60
247
117
55
0
65
53
224
72
57
IQO
108
0
111
60
210
119
54
0
65
53
187
73
58
ivo
1 llfi
166
0
111
60
179
120
54
0
65
53
156
75
59
1UU
141
141
0
111
60
154
121
53
0
65
53
131
77
60
HI
117
117
0
111
60
131
123
51
11-4
65
53
108
80
61
QQ
98-5
0
111
60
113
125
49
7*5
65
53
89*9
82
62
03 .R
82-7
30
111
60
97 3
128
47
96
65
53
75*0
86
62
OO v
70-5
69'6
16*0
111
59
84-9
130
45
7*6
65
52
63*0
90
61
600
580
0
111
59
740
133
42
9*2
65
52
52*7
96
60
40-6
48*3
0
111
59
65*1
136
39
130
65
52
44*7
102
58
41-7
40*2
0
112
58
58*4
140
36
9*8
64
51
381
108
55
36*2
33*4
0
112
58
52 4
144
33
5*9
64
50
33 7
117
49
29-5
27*3
0
112
57
47*4
148
29
0
64
50
30*3
126
44
24-7
22*0
0
113
56
43 4
152
25
0
63
48
27*9
135
36
20*8
17-5
0
114
54
40*2
157
20
0
62
46
26*5
144
28
17*5
13*5
0
116
51
37*7
161
16
0
61
43
26 1
153
21
14-7
9*5
0
119
44
35*4
167
11
0
57
35
25*9
161
12
12-3
51
0
125
33
33*1
173
5
0
52
22
26*8
172
4
Sum
19
74
176
THE VELOCITY OF SPORADIC METEORS-II
IX. §4
Table 48 (cont.)
V
km./aec.
v
km./aec.
B
B
s.
V
km./aec.
B
8
i
S
3
V
km./aec.
3
8
P
= 225°
P
= 315°
deg.
deg.
deg.
deg.
+
deg.
n
deg.
+
deg.
+
281
281
0-8
48
□
262
53
22
11
129
27
301
133
25
235
235
1-5
48
o
216
54
22
11
129
27
255
134
25
198
198
00
48
20
180
55
22
H
129
27
218
135
24
166
166
00
48
20
148
57
23
0
129
27
180
136
24
141
141
00
48
20
123
58
23
0-1
129
27
161
137
23
117
117
00
48
20
99-8
61
24
0-0
129
27
138
139
23
99
98-5
8-4
48
20
81-9
64
24
00
129
27
120
140
22
83-6
82-7
37-8
48
669
67
25
3-0
129
27
104
142
21
706
69-6
47-8
48
20
54-6
72
26
50
129
27
91-3
144
20
690
680
35 3
48
20
44 2
78
27
5-6
129
27
80-2
146
19
49 6
48*3
25 1
47
19
35-5
85
26
68
130
26
71-2
149
17
41-7
40-2
20-1
47
19
29-5
95
20
6-9
130
26
63-0
161
16
35-2
334
16 7
47
19
25-5
106
25
9-7
130
26
57-3
164
fn
29-5
27-3
10 5
46
19
22-5
119
23
112
131
20
520
157
ftl
24-7
220
LU
46
18
21-5
132
18
13 0
131
26
47-2
160
Pi
20-8
17-5
M
45
17
21-3
145
14
Ka
131
25
43-3
162
10
17-5
13-5
LL
43
15
22-0
156
IS
133
24
40-2
166
8
14-7
EJ
12
23-2
165
wi
03
136
22
37-2
170
0
12-3
C3
33
6
25-4
D
00
143
18
34-2
175
3
Sum
EL
72
Table 49
Distribution of Heliocentric Velocities t
V km./aec.
limit$
P
V km /aec.
limits
P
136°
186°
196°
225®
135®
105"
196®
226®
l
163*
i
• •
..
123®
• •
8
+ 11*
8
• •
• «
+ 48®
• •
29-8..
n
00
14 9..
n
—
—
0-0
_
..261
V
14
O
..12 6
V
••
••
26
• •
i
169°
174*
162®
i
• •
• •
107®
• •
8
+ 8°
+ 6°
+ 11*
8
• •
• •
+ 66®
• •
261..
n
—
00
08
12 6..
n
—
—
8-7
—
•. 21-1
V
14
13
16
..14-9
V
• •
32
• •
i
161*
167®
• •
<
121®
ilrjE
• •
8
+ 24°
+ 12®
• •
8
..
WJEm
• •
211..
n
—
—
14-9. .
n
—
—
..17-7
V
10
••
..17-7
*
..
28
• •
*
136°
155®
• •
/
«
106®
• •
8
+ 40’
+ 21®
• •
8
..
+ 68®
Wy $
17-7. .
n
—
00
2-2
—
17-7..
n
—
0-0
..14 9
V
• •
24
20
••
. .21-1
V
••
34
42
• •
f The data for V < 29-8 occur twice, representing different heliocentric directions.
A dash indicates that the corresponding limits of V cannot occur at given P.
IX. 5 4
THE WORK OF OPIK
177
Table 49 (coni.)
9505.06
N
178
THE VELOCITY OF SPORADIC METEORS—II
IX, §4
Table 49 (cont.)
nrii.jovv.
limit*
15°
45°
76°
105°
135°
165°
195°
226°
255°
285°
315°
346°
i
138°
121°
106°
95°
75°
[S3
34°
67°
87°
116°
Kg
148°
s
+ 40°
+ 63°
+ 64°
1+68°
+ 59°
+ 29°
+ 23°
+ 20°
+ 20°
+ 30°
141-7.. n
00
00
0-0
5-0
00
■31
0 6
..188-5 v
134
142
150
155
166
180
173 |
160
145
134
131
i
136°
119°
103°
92°
72°
33°
54°
84°
112°
136°
146°
$
+ 42°
+ 54°
+ 66*
+ 68°
+ 57*
1 +38°
+ 28°
+ 22°
+ 20°
+ 20°
+ 24°
+ 32°
> 168-5 n
0 0
0-0
0-0
00
0 0
06
2 3
KU
00
00
V
200
210
220
220
230
1 284
LJ
252
224
230
1 200
200
The final data in Table 49 can be conveniently summarized to give the
distribution of heliocentric velocities for all directions as shown in
Table 50.
Table 50
Distribution of Heliocentric Velocities for all Directions
12-5
14-9
17-7
211
25-1
29-8
354
42 1
50-1
69 6
70-9
84-3
100-2
1192
141-7
168-5
200-5
238-3
283 3
All
Semi-major axis a
n
%
055
057
061
067
0-77
1 00
1-71
15 3
8-6
3-2
35-9
44 5
138-6
11
0-6
0-2
2- 5
3- 1
9-6
2408
16-8
oo
278-1
19-4
• •
223-4
15-6
• •
168-5
11-7
• *
1400
9-8
• •
82-5
5-7
• •
29-9
2-1
• *
4-8
0-3
• •
66
0-4
• •
7-0
0-5
• •
7-6
05
• •
14
0-1
1,436
100-0
For the elliptical meteors the corresponding values a of the semi-major
axis are given. It is of interest to compare Table 50 with the preliminary
distribution given in Table 42, derived before the application of the
detailed analysis of the projection ratios, and with the distribution of
Table 36 for Opik's personal 279 observations. These comparisons are
IX §4 THE WORK OF OPIK
made in Fig. 94. There is considerable difference in detail between the
provisional and final distribution and between Opik's own observations
and the total number of 1,436 velocities. Nevertheless they aU show the
same main feature of a large component exceeding the parabobc limiting
velocity.
Fio. 94. The distribution of heliocentric volocities (all directions) from Opik's rocking-
mirror apparatus during tho Arizona expedition.
... Opik's 279 observations with opproximato solution for the distribution of
spaco volocities.
. The completo 1.436 velocities with opproximato solution for tho distribution
of spaco velocities.
■**- The completo 1.436 velocities with final solution for the distribution of spaco
velocities.
The broad outline of the distribution of heliocentric velocities in
different directions is given in Table 51. The data show only few solar
meteors from the antapex (P = 315°-15°) and few moving upwards
(P = 45°-105°); but numerous solar meteors for the apex (P = 165°-
195°) and downward (P = 225°-285°) directions. The percentage
of solar meteors in Table 51 is 38-8 per cent., of moderate hyper¬
bolic meteors 46-6 per cent., and of ‘high’ hyperbolic meteors 19-6 per
cent.
(iv) The relation between velocity and luminosity. As regards the
relation between velocity and luminosity in the Arizona records, Opik
gives the data of Table 52, which refer to the uncorrected observed
tangential geocentric velocity v and zenithal magnitude m z .
Table 51
y of Solar and Hyperbolic Meteors in the Arizona Data
IX §4 THE WORK OF OPIK
An analysis for heliocentric velocities by using the provisional approxi¬
mation method gives the data in Table 53.
Table 53
Distribution of Heliocentric Velocities for High and Low Luminosity
V km./sec.
<36
42
50
60
72
85
101
120
143
170
£202
All
ro f <0 (n
(m, = 0-6 true)| %
4
35
62
44
3
0
0
0
0
0
6
154
2-6
22-7
40 3
28-6
1-9
0
0
0
0
0
3-9
100
m, > 0 (n
(fi, = 2-5 true) 1%
152
278
228
269
201
102
12
15
16
9
0
1,282
11-8
21-7
17-8
21 0
15-7
80
0-9
12
1-2
0-7
0
100
These figures indicate that bright meteors have a distribution in
velocity different from the faint meteors. There are no bright meteors
in the range V = 72 to 170 km./sec., but only bright meteors for
V > 202 km./sec.
5. The complete observations of Opik—Arizona and Tartu
Eighty per cent, of the Arizona measurements were made by two
comparatively inexperienced observers. In order to obtain a more
homogeneous series of results Opik observed with the rocking-mirror
apparatus in Tartu from the autumn of 1934 to the spring of 1938. He
obtained an additional 506 observations (202 of which were shower
meteors), which, with his previous 279 Arizona observations, made a
total of 785 velocities determined by Opik. This total material Opik
discusses separately in a publicationf which contains a detailed list of
the actual individual observations.
In an effort to improve the accuracy of the Tartu observations Opik
observed through a fixed reticule or grid for recording the meteor trails,
instead of the star maps used in Arizona. Also during the observations
attention was concentrated on the number of apparent waves produced
in the meteor trail by the oscillating mirror. Thus only the duration of
flight was observed and not other details, such as the shape of the
oscillations, as in the Arizona work.
t Opik, E. J., Publ. Tartu Obs. 30 (1941), no. 6. Summaries of the work havo also
been givon by Opik in The Observatory, 68 (1948), 228, and Irish Astr. J. 1 (1950), 85.
In the latter publication Opik states that the observations were continued at Tartu
until the summer of 1941, when tho observing station fell into the front lino of the
fighting forces, where it was damaged by an artillery shell and essential parts of the
apparatus were stolen. No results subsequent to those considered here (up to 1938)
have been published, however.
182
THE VELOCITY OF SPORADIC METEORS—II
IX, §5
(a) Reduction of Observations
In the Tartu observations the rectangular coordinates of the beginning
and end of the meteor trail were measured. Observations of the co¬
ordinates of a number of stars were also made, these being used to
determine the constants in the formulae for the transition from rect¬
angular to celestial coordinates. If L is the length of the trail computed
in this manner, then the angular velocity of the meteor is determined
from the observed number of waves n by
/L
(Oln)’
where / is a personal correction factor. (The frequency of the rocking
mirror was 10 per second.) / was found from observations of 53 shower
meteors to be 0-832 for the Tartu observations, compared with 0-938
for the Arizona observations.
In cases where the duration r was observed the angular velocity is
given by
where/' is a correction factor varying with r from 0-62 (r = 0-05 sec.) to
100 (r = 1-0 sec.) For Arizona /' was taken as a constant = 0-848.
/' again was determined from observations of shower meteors (35 Tartu,
45 Arizona).
This observed angular velocity was reduced to the zenithal angular
velocity w z by using
where cos z is the mean for the beginning and end of the trail. As before
(p. 157) the linear tangential velocity v km./sec. is then given by
v =
hu> x
57-3
(14)
with the height h in kilometres. For a shower meteor of geocentric
velocity v observed at a distance tj from the radiant, the tangential
velocity is
v = v sin tj.
Hence the above equations give the predicted angular velocity of a
shower meteor as
. -57-3
w = v sin ri cos z -t—
h
( 15 )
183
THE WORK OF OPIK
The^equivalent predicted duration adapted to the observed trail length
L is
The average heights of the shower meteors in (If,) and the mean heights
<• notion ofu> in (14) were assumed on the basis of the Arizona he g
a r at ons aXribed previously. For the Tartu work the heights
^creased by a constant amount of 1-9 km. to allow for the afferent
i i Arizona and Tartu stations.
6 The velocity scale was standardized by using the data on 202 shower
meteors (compared with 73 in the Arizona work). By means of e.gh
® c ' shows the correlation between the observed (ta,) and
omnuTed (w ) angular velocity for the shower meteors as observed by
Jhe different'workers for the case of oscillations and durations The
best correlation is that ofOpik's own Tartu observat.ons for oscillations
X L The worst correlations are those in which the durations were
F . mated-an example (R.W., Arizona) is shown in Fig. 96. l<igs. 9o
!nd 96 illustrate weU the dispersion in the fundamental material of the
rocking-mirror observations.
(6) Analysis of the Complete Results
rtoik discusses in some detail the influence of the observational errors
and selection of data, comparing the various Arizona observers with his
own Tartu observations. By various analyses which will not be repro¬
duced here he draws the general conclusion that the effects of selection
and systematic influences of the particular method, as well as the
nersonality of the observer have little influence upon the statistics of
the meteor velocities. He concludes that the observational materia
referring to meteor velocities appears to be well established. Op.k s total
observational data are summarized in Table 54, uncorrected for error
dispersion.
Observed Frequency of Transverse Heliocentric Components of 1 elocity
for Opik's Arizona and Tartu Observations
Velocity km. 1 sec.
0-14
15-21
22-29
30-42
43-59
60-S4
85-119
Over 120
Sporadic meteors
Number
Percentage .
26
4-6
27
4-6
57
9-8
162
27-8
161
27-6
82
14-1
44
7-5
24
41
Shower meteors
Number
Percentage .
20
90
14
6-9
24
119
65
32-2
44
21 S
24
11-9
4
2-0
7
3-5
184
THE VELOCITY OF SPORADIC METEORS—II
IX, §6
Fio. 95. The correlation of tho observed (u» f ) and computed
(u» e ) angular velocity for tho shower meteors observed by
Opik at Tartu using oscillations of rocking mirror. The full
line represents tho true correlations and the broken linos
the approximate limits of possible observational error.
Fio. 96. The correlation of tho observed (t^) and computed (r e ) durations for
tho shower meteors observed by R.W. in Arizona. From estimates of duration
with the rocking-mirror apparatus.
Opik considers that any uncertainty in the final conclusions must be
attributed to the method of interpretation of these results, in particular
to the hypothesis upon which the distribution of space velocities is
derived.
Here there are two contrasting influences. Firstly if a large observa¬
tional error dispersion is assumed, the spread in meteor velocities and the
relative number of high velocities will be small and vice versa. Secondly
if a large spread in projection ratios is assumed, the mean velocity and
the relative number of high velocities will be large and vice versa. Opik
IX. §5
THE WORK OF OPIK
186
roceeds to take certain limiting cases for these two functions in order
toTet extreme limits to the true velocity distribution.
A maximum-error dispersion is obtained by assuming that aU the
deviations of the observed angular velocity from the computed values of
the shower meteors are errors of observation; that is, none of the ‘shower’
meteors are rejected. Some 20 per cent, of the meteors included as
■shower’ meteors may be stray meteors and hence this will certainly be
an overestimate of the error dispersion. The lower limit^the most
probable observational-error dispersion—is obtained from an analysis
which rejects the probable number of stray meteors from the ‘shower’
meteors. The dispersion is then obtained from the deviation of the
observed and computed angular velocity of the remaining, presumably
true, shower meteors.
As regards the limits in the spread of the projection ratios, Opik takes
the maximum concentration to be that derived for the shower meteors,
which are strongly concentrated towards the ecliptic. The minimum
concentration is taken as that derived from the formula
f, =
"l
for values of sin rj from 0 to 1, where t x is the frequency of sporadic meteors,
f for shower meteors. f 0 for all meteors. n 1 the number of sporadic, and
n 2 of all meteors. With ^ = 621, n 2 = 164 (the probable number of
38 stray meteors being subtracted from the shower total). f 2 the concen¬
tration derived for the shower meteors and f 0 the concentration for all
the Arizona meteors, Opik calculates the frequency of sin t? for his own
observations. He considers that this must be smaller than the true
concentration of the sporadic meteors because the 1,436 Arizona results,
used to obtain f 0 , contain a smaller relative fraction of shower meteors
than Opik’s meteors. Also the values used for f, were for the geocentric
velocities which are more concentrated than the distribution of the
heliocentric velocities. Thus it is possible that the value of f, given by
the formula is doubly overestimated, and hence that the true dist ribution
lies between these values and the values obtained for the shower meteors
alone.
Since the direct observational data of the various Arizona observers
are statistically similar to the Tartu data, Opik considers that with the
same method of reduction both the observational series should yield the
same results. He does not, therefore, apply the full complicated method
of analysis, described earlier, to the Tartu data, but by variations in the
186 THE VELOCITY OF SPORADIC METEORS—II IX, §5
basic assumptions he estimates the possible range of uncertainty in the
final results. Opik’s final summarized results for his 583 observations
of sporadic meteors (Arizona 279, Tartu 304) are given in Table 55 and
Fig. 97 for the various possibilities of maximum errors in observational
error and projection ratios.
Table 55
Distribution of Space Velocities for 583 Sporadic Meteors observed by
Opik in Arizona and Tartu
aD = maximum observational error and maximum concentration of projection ratios.
aE = maximum observational error and minimum concentration of projection ratios.
bD = probablo observational error and maximum concentration of projection ratios.
bE probable observational error and minimum concentration of projection ratios.
V km./sec.
uncorrcctcd
corrected \
aD
aE
bD
bE
< 15 0
< (12)
11
fgl
16
0
17-9
(15)
0
0
0
21-2
(18)
25
■9
24
0
25-2
(21)
2
5
0
300
26
4
ml
14
0
35-8
32
64
Sfl
65
17
42-4
39
77
100
50-4
47
trl
188
128
171
57
121
78
104
71-6
69
83
59
84
84-8
83
62
39
66
101
98
mt!
28
26
39
120
116
SslI
10
11
15
144
140
■o
4
6
5
> 171
> 166
*1J
1
12
23
All
583
583
683
583
Short period solar .
n(?< 32)
106
i
124
17
%
182
1-6
21-3
2-9
Long period solar .
n(P = 39)
115
77
100
%
197
13-2
171
11-8
Hyperbolic .
n (F > 47)
362
497
359
497
%
62 1
85-2
61-6
85-2
t Corrected for zenithal attraction an<fc ellipticity of shower orbits used for
standardization.
The summary of the distribution for the wider velocity classes given
at the bottom of Table 55 shows that the relative frequency of the
short-period meteors is very uncertain and depends largely upon the
assumed law of projection ratios; the same applies to the high hyperbolic
velocities (V > 116 km./sec.), but Opik concludes that the relative
gO i
THE work of OPIK
’ .. . , 7 ? _oq V = 98 kra./sec.)
frequency of the intermediate velocities ( ^ and thafc the
does not show variations ^actorUy established,
distribution may be concern! as 1 errors and of
of projection ratios;
oE = maximum ohacrvational error and minimum concentration
of projection ratios;
bD = probable observational error and maximum concentration
of projection ratios;
bE = probable observational error and minimum concentration
of projection ratios.
(c) The Relation between Velocity and Luminosity
The relation between the heliocentric tangential velocity V 0 and the
zenithal magnitude for the combined observations of Opik is given in
Table 56. There is no systematic change in the distribution of luminosity
with velocity—a result which is in disagreement with the combined
Arizona data described in § 4 (6) (iv) above.
6. Criticisms of Opik’s velocity measurements
Although there are various discrepancies in the results of the rocking-
mirror observations described in this chapter, the final conclusion
188
IX, §0
THE VELOCITY OF SPORADIC METEORS—II
Table 56
Relation between the Heliocentric Tangential Velocity V 0 and the Zenithal
Magnitude m z for Opik's Combined Results
V, km./sec.
< 35
35-42
43-50
61-59
60-71
> 72
All
-10 ("
17
15
H
IS
8
10
02
1%
28
24
11
11
13
10
100
+ " 5 {%
53
30
20
20
38
26
15
17
13
10
19
+2 ' 5 {%
04
37
34
20
M
32
202
32
18
17
13
Kfl
10
100
+ 3-6
32
30
17
13
u
22
125
+ 1%
26
24
14
10
17
100
All ("
100
112
89
72
H
102
589
1%
28
19
15
12
8
18
100
reached by Opik is that at least 60 per cent, of the sporadic meteors are
moving with velocities in excess of the parabolic limit. This work of
Opik has been subjected to severe criticism by the groups of observers
whose results lead to a contrary conclusion—namely that the sporadic
meteors are similar to the shower meteors and do not have velocities in
excess of the parabolic limit. The main criticisms of the work have been
made by Olivierf in America and by Porterf and Prentice§ in Great
Britain. Olivierf complains of the absence of a determination of the
velocity of a well-known shower group as a fundamental check on the
reliability of the method, and refers to the peculiar positions of some of
the centres of radiation. He criticizes the method because reticules were
used in making the observations and these force the employment of only
one eye at a time by the observer. Olivier’s wide experience of meteor
observation had convinced him that the reticule method was inferior to
that of direct plotting upon prepared star maps. He then gives attention
to the 279 preliminary results analysed by Opik,|| in particular to the
number of meteors belonging to the well-known major showers. Since
these showers are well spread throughout the year, Olivier considers that
a comparison of Opik's conclusions during these epochs should represent
t Olivier, C. P., Pop. Aatron. 46 (1938), 325.
X Porter, J. G., Mon. Sot. Roy. Astr. Soc. 103 (1943), 134; 104 (1944), 257; J. Brit.
Astr. A as. 60 (1949), 1.
§ Prentice, J. P. M., Rep. Phya. Soc. Progr. Phya. 11 (1948), 389.
|| Opik, K. J., Circ. Harr. Coil. Obs. (1934), no. 388.
189
IX 6 THE WORK OF OPIK
I orison f« hi. results on V™*
r\f thfi failure to observe the major showers ad q ' ■ j
S, aupidun. A. to the cu»of tin* 0t ™ ””
‘Such a result must have causes. These may be sought, tot n «.
method of observing, but I do not think th.s can possibly explam such
abnormal results. I can only assign them, therefore, to a purely ma h
matical way of treating data when a graphical one, with proper sa -
guards! hasT been genefaUy conceded by the best observers to be the
^"prenticet 0 considers that the base line was too short and that the
technique was not accurate enough for the determination ° f
radiants hence assumptions had to be made about the probable mean
ST- radiation. M-| »noind« that Opik'a path. .» »
erroneous that his results had to be based on mere assumptions as to
radiants and mean heights.
The detailed analysis of the visual observations which lead to this
contrary view have been made by Port*r§ and will be described in the
following chapter.
t Olivier. C. P.. loc. cit.
t Prentice. J. P. M., loc. cit. 9 . 7
§ Porter. J. G., Mon. Not. Roy. Astr. Soc. 104 (1944). 257.
X
THE VELOCITY OF SPORADIC METEORS—III
PORTER’S ANALYSIS OF THE BRITISH METEOR DATA
1. The British meteor data
The main analysis of the British meteor data has been made by Porterf
from a total of 2,669 observations, 90 per cent, of which were made by
thirteen first-line observers.^ From these observations a list of 1,253
accordances was compiled, that is observations made by different
observers at the same time, and bearing other evidence of being different
views of the same meteor. The source of these accordances was as follows:
The A. S. Herschel letters to Denning 1877-1900 3G accordances
B.A.A. Journals and Memoirs . . 1890-1914 68 „
Denning’s Notebook§ . . . 1895-1900 133
A. King’s Notebook . . . . 1898-1920 17
B. A.A. Observations. . . . 1921-1931 274
B.A.A. Modem Observations . . 1932-1940 725 „
Total 1253
Only about two-thirds of these accordances show any real agreement
in path, and thus the material finally treated by Porter consists of a total
of about 800 paths.
(a) Observational Details and Method of Reduction
During the period of the observations treated by Porter there was a
distinct change in the method of observation. In the early years the
observed meteor paths were plotted on a map, and the observers un¬
doubtedly concentrated on the brighter meteors with the longer paths.
Although the extended wand, or string, was recommended in 1890|| there
is no certainty that its advantage was fully realized until 1929, by which
time the British observers were quoting coordinates for the beginning
and end of the meteor path, together with points on the path to define
the actual position of the luminous path. In the subsequent years the
method was further improved in the hands of Prentice, particularly by
t Porter, J. G., Mon. Not. Roy. Astr. Soc. 103 (1943), 134; 104 (1944), 257.
x T. H. Astbury, G. E. I). Alcoek. D. Booth, T. W. Backhouse, J. H. Bridger, W. E.
Beeley, H. Corder, Mins A. Grace Cook, \V. F. Denning, A. S. Herschel, A. King, J. P. M.
Prentice, Mrs. F. Wilson.
5 Denning actually computed the paths of some 1,400 meteors but unfortunately
the only notebook recovered after his death contained only the 133 accordances referred
to by Porter.
|| Mem. Brit. Astr. Ass. 1 (1891), 20.
191
x 5 , ANALYSIS OF BRITISH METEOR DATA
St of intersection of one of the observations with the plan. f the
observations of the other observer is found, so that no assumptions
of simultaneity are made.
(b) Reduction of Multiple Accordances
In the sample treated by Porter there were 100 multiple accordances
(the remainder being duplicate). Sixty-one of these gave satisfactory
results on reduction, and Porter§ has used these to estimate the various
errors The mean errors and standard deviations of these results
given in Tabic 57 divided into ‘old 1 and ‘new’ to indicate the change in
observational method from map plotting to the extended wand referred
to above.
Table 57
Mean Errors and Standard Deviations for the Multiple Accordances
120 old observation*
68 new observations
All observations
Error
Mean
Standard
deviation
Mean
Standard
deviation
Mean
Standard
deviation
aR Radiant
t Twist
A, Offset (bog.) .
A, Offcot (ond) .
A£i Sliding orror
(beginning) .
AE, Sliding error (ond)
An Angular path
deg.
-0 06
-0 20
+ 0 06
+ 010
-028
+ 0 04
000
deg.
1 02
307
110
1*28
3 30
3 45
380
deg.
-0 07
-0 19
000
+ 0 06
+ 0 09
-000
-0-16
deg.
1 13
2- 27
065
081
297
2-60
3- 20
deg.
-0 06
-022
+ 0 03
+ 0 09
-0 15
000
-0 06
deg.
1- 47
2- 81
0-96
113
319
316
3 01
AL Path length km. .
Ah, Height (bog.) km..
Ah, Height (end) km..
Aw Speed %
Am Magnitude .
+ 3-7
4-6
46
-4-8
00
21*1
3-5
3-8
382
1-30
+ 0-6
4 2
2-9
00
-0 6
12-3
3 3
2-2
306
1 00
+ 2-6
4 4
4-0
-2-1
00
18 2
35
34
34-3
1-25
The radiant errors are the residuals in the observational equations,
the positive sign indicating that the observed path passed north of the
correct radiant. The actual angular errors made by the observers are
divided into sliding errors A E along the path (positive in direction of
motion) and offset errors A perpendicular to the path (positive if north
of the true path). The twist t is a guide to the accuracy of direction,
computed from the angle between the observed and computed planes of
t Davidson. M., J. Brit. Astr. Ass. 46 (1936), 292.
J Mem. Brit. Astr. -4m. 34 (1942), pt. 4.
§ Porter, J. G. (1943), loc. cit.
192
THE VELOCITY OF SPORADIC METEORS—III X, §1
observation. The offset errors were found to be an excellent guide to
the value of an accordance. Any observations with an offset r.m.s. error
exceeding 0-060 radians were rejected. The average and median errors
for the quantities of Table 67 are given in Table 58.
Table 58
Average and Median Errors for the Multiple Accordances
Averages
Medians
Error
Old
(deg.)
New
{deg.)
Total
{deg.)
Old
{deg.)
New
{deg.)
Total
(deg.)
A R Radiant
1-23
0-78
1-07
10
0-45
0-7
r Twist .
2-47
1-60
2-15
wm
M
1-7
A, Offset (beginning).
0-86
0-49
073
0-35
0-6
A, Offset (end)
0-95
0-57
081
W'SM
035
K 1 mr
A E x Sliding orror
(beginning) .
2-48
2-32
2-41
1-8
1-7
1-7
A E t sliding orror
(•'nd) .
2-71
m
246
22
1-5
1-7
Av Speed % .
29 9
24-9
27-1
29
21-5
23
Am magnitudo
0-98
091
095
075
0-75
0-75
(c) Reduction of Duplicate Accordances
The majority of the meteors in the sample were duplicate accordances.
Comparison between the r.m.s. errors for these duplicate observations!
and those for the multiples is given in Table 59.
Table 59
Comparison of r.m.s. Errors for Duplicate and Multiple Accordances
Ah,
(km.)
Ah,
(km.)
Am
AL
(km.)
Avf
(km./see.)
A E x 1
(deg.)
A E %
(deg.)
Multiples .
KH
4-5
1-05
14 8
11 3
2-81
2-72
Duplicates
6-6
4-9
0-78
12-2
10-1
2-72
2-65
All meteors
6-5
m
0-80
12 4
10-2
2-73
2-65
| In tho later analysis Porter uses Av—the mean difference in speeds—instead of
the percentage Av (Tables 57 and 58).
Porter investigates the error correlations in these data and finds a clear
positive correlation between the sliding errors A E and the apparent
angular length of the path. A possible explanation is that a meteor with
a short path lies in a star field which can be embraced in one glance,
f Porter, J. 0., 1944, loc. cit.
193
X ,! ANALYSIS OF BRITISH METEOR DATA
are readily available for the very bright meteors-and betwe g
^able for analysis from the multiple and duphea,
observations amounted to 298 shower meteorsf and 480 spora
meteors.
2 The relation between height, velocity, and elongation
Porter investigates the correlation between the various phys.cal
quantities of the meteor, but here we shaU be concerned only w.th height
and velocity as involved in a comparison of tho shower and sporad.c
meteors. The dominant factor amongst those affecting the heigh
the elongation of the radiant-smaller elongation giving greater heights.
The chief effect here must be a velocity one, small elongation being
associated with high velocities as seen amongst the variousi shower
meteors. Porter's data on this relation are summarized in Table 60.
Table 60 indicates that the average shower meteor appears and dis¬
appears at greater heights than the average sporadic meteor-a fact
previously well known from Opik'st analysis of the Arizona results.
Porter points out, however, that the two groups are drawn from very
different ranges of elongation and that a comparison can be made only
for groups covering a similar range of elongation and magnitude, buch
a comparison is made in Table 61, where the shower meteors are compared
with the sporadic meteors over the same range of € and m for two groups
_(A) over the same dates, (B) over all other dates.
| Comprising the following showers:
Persoids, July 22-Aug. 6 .
Orionids. Oct. 16-29 .
Taurida, Nov. 2-9
Leonids. Nov. 15-17 .
S-Aquarids, July 27-Aug. 18
o-Capricornids, July 23-Aug. 10
Camelids, Aug. 6-11
Quadrantids. Jan. 1-7
Lyrids, April 13-24
fl-Piscids, Aug. 27-Sept. 18
152
35
28
27
15
14
8
8
6
5
Total 298
X Opik, E. J., Ann. Harv. Coll. Obs. 105 (1937), 549.
O
SM6.M
194
THE VELOCITY OF SPORADIC METEORS—III
X, §2
X, §2
ANALYSIS OF BRITISH METEOR DATA
196
Table 61
ReUUion between Shower and Sporadic Meteors over the sa m e raruje
of e and m
Leonida
c =■ 10-5°
Orionida
« = 241*
Poreoida
« - 39-2°
S-Aquarida
« =» 69-4°
Taurida
« - 81-6°
h,
n
hi
h,
n
hi
h,
n
hi
h,
n
h,
h,
a-Copricomids h,
« ~ 93 0° h,
125-6£2-34
941±200
27
1197±214
100-9±l-79
35
1149±l-32
94- 7±0-98
152
1011 ±4-43
890±4-39
15
101 6±224
77-7±l-97
28
95- 5±4-25
85-3±342
14
Group ( A )
(same dales)
1170±406
9 9-5±2-77
14
108-8±215
93-2±2-73
26
101-9±2-99
84-9±l-96
16
909±4-43
78’8±3‘49
14
100*9±3*24
82-7 ±2-24
13
Group (B)
(all other dales)
121-2±4-52
101-3±317
21
114-4±l-90
101l±l' 65
53
1120±2-56
94-4±2-20
29
100-3±2-23
83-8±2-49
36
98-8±2-94
77-9±194
62
93-3±209
80-5±2-48
37
It is evident from this comparison that the mean he.ght °f ^ower
and sporadic meteors are now significantly the same, that theheight of
appearance and disappearance is determined mamly by ‘ «ul “ a nd
that in this respect both shower and sporadic meteors behave in an
identical manner. . , _ o«
The relation between velocity and elongation is shown m Fig. W,
where the fuU curve is the theoretical geocentric parabohe velocity, and
the results for six showers and nine groups of sporadic meteors are
plotted. The close similarity between the groups indicates that the
velocities of the sporadic and shower meteors are of the same order, he
actual distribution of v/v p amongst the shower and sporadic meteors is
shown in Table 62.
Sixteen per cent, of the sporadic meteors have a v/v p ratio greater than
unity (that is hyperbolic velocity), but this also applies to 14 per cent ot
the shower meteors so that the figures merely represent the tail ot the
distribution curve.
3. Comparison of Opik’s and Porter’s analysis
It is evident that Opik’s analysis of the Arizona results, and Porter s
analysis of the British results lead to opposite conclusions about the
196
THE VELOCITY OF SPORADIC METEORS—III
X, §3
80
70
\
4 60
4 .0
® Leonids \
r.jOrumids\
I.
ifPersei
k
■ ^
•
\
• _
Aquondse
IS&Z&L
•Ns
<u
'°c
r 3
O' 6
O' 5
o* /
20* /
50* /
Elongation £
Fio. 98. Relation between elongation and velocity from Porter’s analysis of
the British meteor date. © shower meteors. • nine groups of sporadic meteors
separated in elongation. -parabolic velocity limit.
Table 62
Distribution of v/v p for Sporadic and Shower Meteors
v/v p
Number of sporadic meteors
Number of shot
00-
2
• •
0 2-
62
25
0-4-
145
77
0-6-
95
85
0-8-
52
36
10-
23
20
1*2-
18
6
1-4-
12
4
1-6-
7
4
1-8-
2
1
20-
7
2
30-
1
• •
existence of a meteor component with hyperbolic velocities. Opik
concludes that some 62 per cent, of sporadic meteors have hyperbolic
velocities, whereas Porter concludes that there is nothing in his analysis
of the British data to justify the belief in more than an occasional meteor
with hyperbolic velocity. Porter’s criticism of Opik’s data has been
referred to on p. 189, while Opikf likewise discusses Porter’s conclusions
on the grounds of the heterogeneity of the basic data. One serious diffi¬
culty to the acceptance of the hyperbolic theory lies in the problem of
t Opik, E. J., Irish Astr. J. 1 (1950), 80.
197
x . 3 ANALYSIS OF BRITISH METEOR DATA
the height range of the Shat the
correlation between height and \elo * at very mu ch greater
£ss —— b
different from that of the shower meters velocity measure-
Evidently an appeal to ne xt two chapters
mentis necessary to overcome tins P , y c radio-echo
we shaU review the contnbutions of the photograp
work to this problem.
t Opik, E. J-, Ann. Harv. CM. Oba. 105 (I 937), M9.
XI
THE VELOCITY OF SPORADIC METEORS—IV
PHOTOGRAPHIC RESULTS
The first successful attempts to measure the velocity of meteors by
using a rotating shutter in front of the camera lens appear to have been
made by Elkin of Yale between 1893 and 1909.t An analysis of Elkin’s
work has been presented by Olivier.J Elkin appears to have recorded
131 meteor trails, but only scanty data could be found for some of the
records. In any case the base lines used by Elkin (3-3 and 5-0 km.) were
too short for accurate velocity measurements and no useful purpose
would be served in giving further details of the work. Subsequently the
photographic work was carried out elsewhere, such as by Lindemann
and Dobson§ in England and by Fedynski and Stanjukowitsch|| in
Russia, but the main results have been obtained by successive workers
at Harvard. In this chapter we shall be concerned mainly with the
Harvard results on the velocity of sporadic meteors.
1. The results of Millman and HofHeit
Meteor photography at Harvard with rotating shutters was initiated
by Fisher, who used two cameras fitted with Ross Xpress F/4 lenses of
6 in. focal length. Fisher obtained preliminary photographs with this
equipment and assigned the programme to Millman in 1932. The first
published analysis by Millman and Hoffleitf t concerns fourteen meteors
photographed between 1932 August and 1936 July—one successful
photograph being obtained for approximately 90 hours of exposure time.
(a) Reduction of Data from the Photographic Plates
The photographic meteor trails obtained by Millman and Hoffieit were
segmented by the operation of the rotating shutter which occulted
the lens 20 times per second. The determination of the velocity of the
meteor was made in the following manner. In Fig. 99, L is the camera
lens, which, in the present analysis, is assumed to be distortionless. AB
is the meteor in the atmosphere and PQ the image on the photographic
plate. Let A and P be fixed points on the trail and plate respectively and
t Elkin. W. J., Astrophya. J. 9 (1899), 20; 10 (1899), 25; 12 (1900), 4.
x Olivier, C. P., Aatr. J. 46 (1937-8), 41.
§ Lindemann, F. A., and Dobson, G. M. B., Mon. Not. Roy. Aatr. Soc. 83 (1923), 163.
|| Fedynski, V., and Stanjukowitsch, K., Aatr. J. UJS.S.R. 12 (1935), 440.
tf Millman. P. M., and Hoffloit, D.. Ann. Horv. Coll. Oba. 105 (1937), 601.
199
PHOTOGRAPHIC RESUL
B and Q variable points moving in the diction of the arrows,
with the geometrical construction as shown.
x\z __ r+d
s “ r
y+r+d, y+r
ir V «Wa K - — — — is a constant for a given
Hence x = where K - - - p
If the meteor has constant velocity v, then x — vt and
t _Ki.
v i i+r*
also
d y __ (y+ r ) a where — = C (constant),
dt Or
uu v/f
Differentiating, **■« a straight line relation
between ^ and y. In principle these quantities can be found from
the plate measurements, and the constants, and C
radiant point and geocentric velocity of the meteor. If mstead of
constant velocity, a constant deceleration v is assumed, then (vt- - )
is substituted for x, and the relation between and y becomes
more complicated and deviates from a straight line.
Unfortunately a very small error in measurement leads to a large
percentage error in the second derivative and the measurements
200
THE VELOCITY OF SPORADIC METEORS—IV XI, §1
made by Millman and Hoffleit were not sufficiently accurate to justify
its use.
A simplification ensues because the trail is generally short compared
with its distance from the radiant, that is, y small compared with r.
In such cases higher powers of y with respect to r can be neglected
and we obtain ,
dt C y+ C’
which is a straight line relation between dy/dt and y with slope
2
S = q and intercept on the y-axis Y =
Y and S are obtained graphically or by least squares, r and C are thus
determined, p and the angle at P are obtained from plate measurements,
then 8 can be computed. If the distance of the meteor from the camera,
o, is known, the velocity v is then given by
K
C “ 2 p'
For the case of constant deceleration
dy
dt
(neglecting higher powers of y),
which is also a straight line relation between dy/dt and y, with slope
S' = * *
C V
and intercept
Hence
and
Millman and Hoffleit did not have sufficient data available to evaulate
any possible deceleration and based their computations on the assump¬
tion that the meteor was moving with constant velocity when the curve
between dy/dt and y was a straight line. The procedure was to measure
the distances between successive breaks and to determine the velocity
from the plot of dy/dt against y, as indicated above.
Y' =
—rv
2v—vC*
-
V =
S'os
V 08
2 p v 2 p
XI. §1
PHOTOGRAPHIC RESULTS
201
(6 S“f the meteors analysed by Millman and Hoffleit were either
Perseids, Leonids, or Orionids. The remaining seven sporadic meteors
are listed in Table 63. f .
Although such photographic measurements are capable g
accuracy the present analysis suffered because for all the meteors listed
in Table 63 only one camera was operating and hence no heig me *
ments were obtained. The heights quoted are assumed heights based
on early data given by Opikt for the relation between height, magnitude,
and velocity.
Table 63
Data on Seven Sporadic Meteors photographed by Millman and
Hoffleit between 1932 and 1936
Meteor
No. f
Date and Time
(E£.T.)
Magnitude
{zenithal
at 100 km.)
Radiant
(1900)
Elongation
from apex
e {deg.)
Height
km.
V•
kn
tloei
\-l*e
'vt
c.
«(**)|
h{deg.)
v
v «
V
75
+ 45
67
68
26
24
305
339-5
-1-6
93
66
20
16
36
I 4
3606
+ 43-2
85
62
13
6
30
20 6
+ 111
92
60
14
8
31
— 9
183 0
+ 18 6
21
70
72
71
44
238
— 7
17
70
55
64
27
1 -•
247-8
+ 34 7
115
60
15
10
36
6 I 1933 Nov. 16d. Oh. 38m.
7 | 1935 Sopt. 7d. lh. 36m.
1936 Sopt. 30d. 20h. 28m.
1936 Oct. 20d. lh. 04m.
1935 Doc. 29d. 4h. 36ro.
1936 Fob. 29d. 4h. 08m.
1936 July 6d. 23h. 65m.
+ Catalogue number correaponding to the nomenclature of Millman and Hoffloit.
tv — observod volocity relative to the oarth.
v. - obsorvod volocity v corrected for aonith attraction.
- holiocentrio velocity obtained by correcting v, for the earth a motion. .
§ The speed of rotation of the shutter was uncertain during this photograph, and tho velocity
may bo double tho value given.
The times given are the mid-points of the exposure times of the plate,
which varied from 71 min. to 120 min. The magnitude was estimated
for the brightest part of the trail by photometry.
The heliocentric velocities V computed for these seven sporadic
meteors are well below the parabolic limit with the exception of No. 12
for which the parabolic limit is just exceeded. Similar analysis of the
seven shower meteors indicated that there may have been a loss in
velocity of some 10 km./sec. due to deceleration. Even if allowance is
made for this, only two more of the velocities are raised slightly above
the parabolic limit, and there is little indication of the very marked
hyperbolic velocities to be expected on the basis of Opik’s work.
t Opik, E. J., Proc. Nat. Acad. Sci. Wash. 22 (1936), 526.
202 THE VELOCITY OF SPORADIC METEORS—IV XI, §2
2. The results of Whipple
In 1936 Whipple instituted a new two-camera programme at Harvard
for meteor photography. His results represent the first real precision
measurements in meteor astronomy. The definitive orbits which he was
soon able to give for the Taurid and Geminid showers are amongst the
highest achievements in the subject. This work on the shower meteors
will be considered in Chapter XV; here we are concerned only with
Whipple’s data on the sporadic meteors.
The two cameras were situated at the ends of a 38-km. base line; the
AI patrol camera at Oak Ridge, and the FA patrol camera at Cambridge.
Both cameras were equipped with Ross Xpress lenses of 6-9 in. focal
length and aperture 1*5 in. The occulting shutters gave 20 interruptions
per second. The routine observing programmes were synchronized so
that the two cameras were directed towards a point in space about 80 km.
above the earth’s surface.
(a) Reduction of Data
In the firstf of the publications dealing with this work, Whipple
describes in detail the method of measurement of the segmented trails
on the photographic plate and the treatment of the data. The apparent
radiant was determined by measurement of the trail position relative
to several faint stars symmetrical about the trail. The plate centre was
determined from the position of three stars by a method due to Olmsted J:
and from this centre standard coordinates were determined for all the
stars according to Turner’s method.§ These coordinates were related
to the measured coordinates by means of a number of comparison stars
of known coordinates distributed along the trail, at small distances from
it. Hence, theoretical coordinates for each star measured on the plate
could be calculated. The differences between these and the measured
coordinates give the corrections necessary for lens distortion, and also
for measurement errors, and the effects of differential refraction.
Whipple considered that the radiant coordinates determined from the
photographic plates were correct to an accuracy of 2 minutes of arc.
For a doubly photographed meteor the height of any point of the
trail can be determined from the direction of the trails on the two plates,
provided the time of appearance of the meteor is known. This latter
presents some difficulty with long exposures except when the meteor is
also seen visually. Otherwise it is necessary to determine the times of
f Whipple, F. L., Proc. Amcr. Phil. Soc. 79 (1938), 499.
1 OlmsUxl. M., Ann. Harv. Coll. Obs. 87 (1931), 221.
§ Turner, H. H., Mon. Sot. Roy. Astr. Soc. 60 (1900), 201.
203
XI g 2 PHOTOGRAPHIC RESULTS
appearance by identification of natural irregularities in the trails as
seen from the two stations. This determination is the least satisfactory
part of the early measurements. For example, in the first six results
described by Whipple,t one meteor was also seen visually and hence an
exact time could be given, but accurate times could be found only lor
two others. In one case of a faint trail (No. 660), the possible time of
apparition extended for the duration of the exposure (60 mm.). Ihe
detailed method of height computation depends on the position of the
intersection of the two planes passing through the stations and not on
the identification of points on the two trails. The method of computation
whioh is due to Schaeberle has been described by Olivier.J
The coordinates of the shutter breaks on the trails were transferred
to a distance s along the actual trail in space by the method of Millman
and Hoffleit described in § 1. An example to illustrate the accuracy
obtainable is given in Table 64 for a single meteor (No. 642). The first
column gives the time in mean seconds from the first break, the second
column the square root of the weight assigned to the measurement,
based on the appearance of the breaks at the time of measurement.
Three types of equations were then fitted to the measured distances, 8,
by means of least squares:
s = A+Bt+Ct*,
8 = A+Bt+Ct 3 ,
s = A+Bt-f Ce ct ,
( 1 )
( 2 )
( 3 )
where A, B, and C are unknown constants, and c is a constant arbitrarily
chosen for each meteor. The last three columns of Table 64 give the
residuals from the solutions according to (1), (2), and (3). It is to be
expected that equation (3) would represent most accurately the motion
of a meteor in an atmosphere in equilibrium with gravity, since the
exponential increase of density with decreasing height should produce
an exponentially increasing deceleration, c was estimated for each
meteor on the assumption that the air resistance was proportional to
the density. The velocities and deceleration of this meteor calculated
according to the three equations are given in Table 65.
It is evident from the data in Tables 64 and 65 that the three equations
fit the observations equally well, and the same is true for the other
meteors discussed by Whipple. Whipple concludes that the observed
t Whipple, F. L. (1038), loc. cit.
x Olivier, C. P., Meteors, ch. xiv, Williams & Wilkins (1925).
204
THE VELOCITY OF SPORADIC METEORS—IV
XI, §2
Table 64
Example of Whipple 1 a Trail Coordinates and Residuals for Meteor
No. 642
Time from
first break
t (etc.)
^(Weight)
Distance along
trail in space
a (km.)
Residuals for equations (1)—(3)
o-c
eq. (1) (km.)
O-C
eq. (2) (km.)
O-C
eq. (3) (km.)
0-00
0-3
0-0000
-0-0594
-0-0795
-0-0832
0-8
1-6339
+ 0 0098
+ 0-0037
+ 0-0014
0-10
0-8
3-1884
+ 0 0065
+ 0-0087
+ 0-0082
016
0-8
* Jt t Y i •
+0-0046
+ 0-0105
+ 0-0119
0-20
-0-0077
-0-0015
+ 0 0010
0-30
-0 0097
-0-0071
0-36
0-8
10-8697
+ 0 0004
-0-0024
0-40
12-3916
+ 0-0052
+ 0 0024
0-46
0-8
13-9083
+ 00116
+ 0-0056
+ 0-0018
0-60
0-8
16-4094
+ 0 0091
+ 0-0059
+ 0-0026
10
16-8928
-0 0042
-0-0004
+0-0012
0-60
0-3
18-3470
-0 0399
-0-0238
-0-0094
Probable errors of observation (weight unity) ±0-0067 ±0-0067 ±0 0005
Table 65
Velocities and Deceleration of Meteor No. 642
Mid-
time
M«ec.)
VdocHy
v#
(km./see.)
Accelera-\
lion
Equa¬
tion
A (km.)
B (km.)
C (km.)
l
(1)
(2)
(3)
+ 0-0594
+ 0-0795
+ 0-1036
+ 31-3612±0 0626
+ 31-0172 ±0-0382
+ 31-1016± 0-0426
-1-3690 ± 0 0992
-1-4770 ±0-1068
-0-02031 ±0-00142
• •
Li
0-300
0-300
0-300
30646
30618
30646
-2-718
-2-669
-2-276
-0 089
-0-087
-0-074
decelerations are consistent with an assumption that the density
decreases exponentially with height, and utilizes the observed decelera¬
tions to determine the absolute values of the density. In any case it is
seen from Table 65 that the calculated velocities v 0 at the mid-point
are almost independent of the law of deceleration assumed, and that the
decelerations are only slightly dependent on the law.
Finally the velocity v 0 has to be reduced to the corresponding velocity
V for the case of no atmosphere. Whipple applies the equation
l°gV = logv 0+ 9 -l^[log(l-9-73xl0-^)],
where z is the true zenith distance of the radiant and e.g.s. units are used.
205
PHOTOGRAPHIC RESULTS
XI. 3 *•
(b) Whipple's Analysis for Seven Sporadic Meteors ,
‘ Whipple 'a analysis of the results with the
have so far been given in six publications (o) (/)-t ’ ,
St “^3
rsasit
-K STZSS ZZZXZX-Zgz
« 3 ) The data given in (6) for Nos. 505 and 756 were obtained from
the sinuosity of the trails in two double cameras, caused by vibration
ofTcamera supports. The reduction of the data is the same as or
the occulted lens systems. Table 66 contains the essential Published
information on these seven meteors. The most complete data are given
in the 1938 publication for meteors 642, 660, 663, 670, 694. The
for numbers 605 and 756 are given in the 1940 publication and the in¬
complete data for number 694 in the 1943 publication
For three of the meteors (660, 663, 505) the times of apparition are
uncertain, and solutions for the extreme ranges of possible time are
given in each case. The following notes, numbered to correspond with
the entries in Table 66, explain the data which are not self-evident:
(vi) The magnitudes were determined from a comparison of faint star
images in the vicinity of the trail. The effective exposure times
varied from 4x 10-* sec. for a fast meteor to 8x 10 3 sec. for the
star images. Whipple* discusses the possible failure of the recipro¬
city law and other matters relating to the magnitude estimates in
some detail.
(vii) Q is the angle between the poles of the great circle motion as
seen from the two stations. sinQ represents the relative accuracy
with which the apparent radiant is determined for equal precision
in the determination of the great circle motion. The trail length
multiplied by sinQ is an approximation to the relative accuracy
of the apparent radiant. The data in Table 66 indicate that all
the radiant determinations have an accuracy of about two minutes
of arc.
and Whipple, F. L., Tech. Rep. Harv. Coll. Obs., no. 6 (Harvard Reprint Senes U-35),
1950.
X Whipple, F. L. (1938), loc. cit.
Table 66
Whipple's Double Station Data for Seven Sporadic Meteors
206
THE VELOCITY OF SPORADIC METEORS—IV
XI, §2
3 *
fils =° + ? s 5 s s+ S a a s=°°ssa»"
S| = :: I : l s 3 : | || ■■I I :
n 3?J ■???«
® 9n-®r»LVoM
• 3” oow £§g
*-? S : S »o o : w : :L 5 ;
7 $ S 5 S 3 + 22
: 5 g •
§a
2
i +
9 lomoo «cpo»)
5 ” oos ira-
j . -—-o
|II s Jl a 3S 0 SS ?Jsfc S & I Siflgfe!** |
| 2 .-c. «oo - 8g - - 8 i su- s a a a r”<;V- 2
«- _ -* T T * x ^
1 : : : : : : :f ? gf 8 : : «M $ I
g ° o «8 5 |58 3 3 5 S^°°27g2S
jig g oi§ 3 ss "' 2 I i s iisil .***
fl*” 6 7 + + 3 22 5 |ss 2 2 2 st 6 *J , M&
O £r-
c^o. Isa- .. M sii§? b * 2 -- 1
.| a s| 3 " b '~s a a s :
|li a J1 s s
“§-S5* § 3
O ~
2 ss r? rr? s i s saiiSrT^r 5
8 55 2 82 2T5 2 2 * 5 NOOCO T2S'' 5 .
+ 1 - £
jjNOOwVojJ* |
322°
2 sis’*
1 -
IS? ?
«|S°2°
I - 1-31 , 4 1 i
• If 1 " #i fa 1 "1"i'«v !•••■*••••
■ lilli • •! -J -1? • • ■l|-“
sg lit? ip 3 if § | iifit fliim
207
XI §2 PHOTOGRAPHIC RESULTS
(viii) z is the zenith distance from Oak Ridge.
(ix) to (XU) Heights refer to the horizon plane through Oak Ridge.
Height at maximum refers to the brightest part of the trail, mclud-
ing flares.
(xiv) Corrected radiant obtained by correcting the apparent radiant
successively for the aberration effect of the earth s rotation and fo
zenith attraction.
(xv) e is the elongation of the corrected radiant from the apex of the
earth’s way.
(xx) to (xxvii) Notation according to Chapter V.
(c) Discussion of Whipple's Measurements on the Seven Sporadic Meteors
The fundamental accuracy of Whipple's data given in Table 66 can be
checked against the data which he derives for the shower meteors with
the same photographic system and analysis-t The agreement m the
velocities shows that the velocities determined by the rotating shutter
method are not subject to large errors produced by deceleration in the
atmosphere as suggested by Millman and Hoffleit.* The comparisons
also show that tho correction for atmospheric deceleration discussed m
(a) above is of the right order.
The velocity results show that the sporadic meteors 642, 660,670, 694,
505, 756 are moving in short-period elliptical orbits around the sun. In
the case of 663, however, there is an uncertainty of 20 minutes in the
time of appearance of the meteor. Whipple§ states that the natural
irregularities in the trails were difficult to measure and no certain
identification could be made. From repeated trials with two different
matching techniques it seemed that the sidereal time of lOh. 20m. was
correct. This implies a marked hyperbolic velocity (78*9 km./sec.
geocentric, 51-8 km./sec. heliocentric). On the other hand Whipple
considers that the various physical data of the meteor compared with
the others indicates a solar system origin and his final decision is agamst
the hyperbolic value. The other extreme of the solution for this meteor
yields a velocity less than the parabolic value (67-7 km./sec. geocentric,
40-8 heliocentric). Opik’s views on these results will be referred to
later (§ 4).
f Whipple, F. L., 1938, 1940, 1949, loc. cit. See also Chapter Xm et. soq.
x See this chapter, § 1.
§ Whipple, F. L., 1938, loc. cit.
208
THE VELOCITY OF SPORADIC METEORS—IV
XI, §3
Table 67
Additional List of Sixteen Sporadic Meteors extracted from Jacchia’s f
First Analysis
Meteor
number
Date
Number of break*
in trail
Velocity
km. 1 sec.
Acceleration
km./eec.*
663$
1937 Feb. 12-22
18
Mi?' 1 Mi
98-6
816
1939 Jan. 24-11
13
61-6
828
1939 Mar. 20-16
24
80-4
982
1940 Aug. 29-20
11
91-6
1006
1940 Oct. 27-07
11
26-74
86-2
f 9
22-59
-2-84
67-2
1068§
1941 Mar. 23-08
I 11
21-65
-500
62-8
1 9
19-77
-10-07
68-8
1071
1941 Mar. 31-34
16
67-33
-3-23
84-2
1103
1941 Nov. 26-38
8
76-49
+ 1-06
94-7
1170§
1942 Aug. 2-20
5
6
67-93
67-35
-7-07
-25-63
90-6
90-0
1180§
1942 Oct. 4-15
'22
10
20-39
19-98
-0-743
-3-85
79-4
73-3
1205§
1943 Mar. 26-23
*22
18
33-10
31-85
-0-437
-6-25
74-6
61-3
1241
1944 Dec. 10-07
24
29-14
-1-37
79-1
31
11-98
-0-178
1242§
1945 Feb. 6-22
34
38
11-62
10-52
-0-672
—1-316
64-6
46-1
17
9-35
-1-941
41-8
19
28-05
— 1*19
781
1243§
1945 Feb. 6-30
*
20
25
27-03
27-20
-2-98
-3-74
66-1
66-1
24-65
57-1
1614
1947 Oct. 12-30
32
13-52
gam*
66-4
20
2504
85-5
21
24-86
79-6
1644$
1947 Dec. 10-01
«
21
24-44
73-2
19
23-43
67-0
15
21-50
62-4
1666$
1947 Dec. 17-35
22
19
35-07
34-75
HI
92-4
88-0
f Jacchia, L. O. (1948), loc. cit.
x Included also in Table 66—see note in text.
§ The reason for the alternative solutions is not given. They are presumably
either due to timing uncertainties or split components of the trail.
3. Jacchia’s analysis of the double-camera data
In two reportet on ballistics and upper atmospheric air densities
Jacchia gives the most complete list of velocities, determined by the
double-camera system, which has yet been published. The 1948 reportf
gives a list of 50 velocities, 14 of which have been previously published by
t Jacchia. L. G., Tech. Rep. Harv. Coll. Ob*. (1948), no. 2 (Harvard Reprint Series,
11-26); (1949), no. 4 (Harvard Reprint Series, H-32).
209
XI § 3 PHOTOGRAPHIC RESULTS
Whipple (§2 above). The remaining 36 contain 16 sporadic meteors
which are listed in Table 67. Most of these were photographed using the
two-camera system employed by Whipple at Oak Ridge (AI) and Cam¬
bridge (FA) with shutters rotating at 600 r.p.m. After August 1947
some results were obtained with new, unguided cameras—KA at Cam¬
bridge, KB at Oak Ridge. These each used Kodak-Ektar lenses of 7-in.
focal length and aperture F/2-5, with shutter speeds of 1,800 r.p.m. (KA)
and 1,200 r.p.m. (KB). In the summer of 1948 these cameras were
removed to sites in New Mexico at Dona Ana and Soledad Canyon.
The data given by Jacchia for these meteors are rather incomplete
compared with the data given by Whipple in Table 66. The velocities
correspond to the apparent measured velocities v 0 of Table 66, and the
heights to the point for which v 0 is given (corresponding approximately
to ‘Height at middle’ of Table 66). Unfortunately no data are given for
the computation of heliocentric velocities or orbital elements. One
meteor (1103) has a velocity of 75-49 km./sec., which is in excess of the
geocentric parabolic velocity. The much disputed meteor, number 663,
is also included in Table 67 since Jacchia gives a value for v 0 almost
exactly at the parabolic limit, intermediate between the extremes
quoted by Whipple in Table 66.
Jacchia’s 1949 report t gives a list of fifty-two meteors photographed
in the double-camera programme. Forty-two of these are repeats of
previously published data. The relevant velocity information on the
remaining ten is given in Table 68, but there is no indication as to whether
the meteors are shower or sporadic.
Table 68
Additional List of Ten Velocities extracted from Jacchia's Second Analysis f
Meteor number
Velocity km. 1 sec.
Height km.
808
3631
93-8
1065
4909
113-2
1158
29-85
90-5
1270
60-25
106-3
1360
71-78
107-3
1447
72-28
105-3
1472
68-88
103-9
1542
23-71
77-5
1650
3664
95-8
1687
68-39
105-1
4. Discussion of the photographic velocities
The double-camera photographic technique is capable of such high
accuracy that it can, in principle, settle the hyperbolic velocity problem
f Jacchia, L. G. (1949), loc. cit.
P
3595.68
210 THE VELOCITY OF SPORADIC METEORS—IV XI, §4
without ambiguity. Unfortunately, with the types of camera so far used,
the collection of data is a long task since only very bright meteors can be
photographed satisfactorily. Even in the cases of the meteors already
photographed the unfortunate ambiguity in the time of appearance of
number 663 has perpetuated the dichotomy of views as to the reality of
the hyperbolic component. Further, in the most complete published
lists (those of Jacchia, Tables 67 and 68) there is no information which
enables the heliocentric velocity to be computed, but, even so, one
meteor (1103) has a velocity exceeding the geocentric parabolic limit,
and two others (1360 and 1447) are at the limit.
Whereas the adherents of the solar system origin for meteors point to
the lack of any very high velocities such as found by Opik (Chap. IX),
Opikf accepts the photographic data as proof of the hyperbolic theory.
Whereas WhippleJ considers from physical evidence that the low
elliptical velocity for meteor 663 is correct, Opikf investigates the rela¬
tion between luminosity and velocity in Whipple’s data and concludes
that meteor 663 fits this relationship well when it is given the hyperbolic
velocity; but that it lies six magnitudes away from the curve connecting
magnitude and velocity when the lower elliptical velocity is assigned.
Opik also criticizes the photographic results on two other grounds:
(i) that the preponderance of shower meteors in the photographic
results, compared with his visual Arizona results, indicates that
the solar component amongst the bright meteors is strongly
enhanced;
(ii) that the photographic selection favours meteors with low angular
motion across the photographic plate.
5. The future of the photographic programme
The failure of the double-camera technique to provide an unambiguous
answer to the velocity problem has been due basically to the fact that
the techniques used were restricted to very bright meteors. Firstly, this
implies that the collection of sufficient data is a prolonged task since
with the AI and FA cameras it required an average of some 100 hours
exposure to obtain a satisfactory duplicate photograph. Secondly, the
results are open to a criticism that they refer to very bright meteors,
which may possibly represent a different selection of the meteoric
material than the visual observations referred to in Chapters IX and X.
The development and construction of Super Schmidt cameras to
t Opik, E. J., Irish Astr. J. 1 (1950), 80.
x Whipple, F. L. (1938), loc. cit.
211
XI, $6 PHOTOGRAPHIC RESULTS
overcome these basic difficulties has been described by Whipplef and
have been discussed in Chapter II. The magnitude limit is expected
be reduced to about +4 compared with zero to -1 on the existing
instruments. Table 69 gives the anticipated details of characteristic
and performance compared with the various cameras used for the worK
described earlier in this chapter.
Table 69
Anticipated Performance of Super Schmidt Camera compared with
existing Cameras
Camera
Aperture
(in.)
Focal ratio
Field diameter
(degrees)
Light
transmission f
Performance
meteors /100
hours
Ross Xpress
Cooke Taylor .
3-in. Ross
Aoro-Ektar
Super-Schmidt .
16
1-5
30
30
120
4
8
7
2-5
0-85
60
33
20
45
62
10
M
0-8
0-4
1-3
10
0-3
0-7
2-3
260
t Rosa Xpress takon as unity for comparison.
Allowing for the increasing ‘dead time’ due to the more frequent film
changes required—even on a perfectly dark night the limiting exposure
is expected to be about 15 minutes—WhippleJ estimates that the yield
per annum should be increased by some 40 times on the existing instru¬
ments, and anticipates satisfactory double station information from
about 100 meteors per annum.§ According to a recent announcement!!
the construction of two of these Super Schmidt instruments was com¬
pleted by the Perkin Elmer Corporation during 1951. The first was
installed at Soledad, New Mexico, during the summer of 1951. The
results from these instruments, which should give a precise answer to
the problem of the hyperbolic velocity component, will be awaited with
interest.ft
t Whipple, F. L., Sky and Telescope, 8 (1949). 90; Tech. Rep. Harv. Coll. Obs. (1947),
no. 1.
x Whipple, F. L. (1949), loc. cit.
§ Whipple, F. L. (1947), loc. cit.
|| Sky and Telescope, 10 (1951), 219.
tf In a private communication received at the end of October 1952, Dr. Whipple
stated that the Super Schmidt cameras were working excellently, and that in September
1962 nearly 200 doubly photographed meteors wore obtained. It is therefore evident
that the photographic meteor studies have entered a new epoch and that the informa¬
tion givon in this chapter will become of historic interest only during the course of the
next few years.
XII
THE VELOCITY OF SPORADIC METEORS—V
THE RADIO-ECHO RESULTS AND GENERAL CONCLUSION
In the previous four chapters we have seen that the conventional visual
and photographic techniques have led to an impasse over the question
of the velocities of sporadic meteors. The new radio-echo techniques for
the measurement of velocities, developed in the years following 1945
(Chaps. HI and IV), have since been applied to this problem indepen¬
dently in Great Britain and Canada. The workers in Great Britain used
the pulsed techniques with narrow-beam aerials in order to select
particular groups of sporadic meteors; whilst the Canadian workers used
the continuous-wave techniques with wide-beam aerials. The details
of the two programmes and the results will be discussed separately in
this chapter.
1. The work of Almond, Davie9, and Lovell
(a) Equipment
The measurements in Great Britain have been made at the Jodrell
Bank Experimental Station by Miss Almond, Davies, and Lovell.t The
radio apparatus was essentially similar to that described in Chapter IV.
The transmitter radiated 600 pulses per second each of 10 microsec.
duration. Since the separation between pulses corresponds to only 260
km. in range it was necessary to double every fourth pulse so that ranges
could be measured to 1,000 km. without ambiguity. Two radio wave¬
lengths were used in a series of four equipments designed successively to
record meteors of fainter magnitudes.
Equipment I
Equipment II
Equipment III
Equipment IV
Wavelength A .
Peak transmitter power P .
Aerial beam width t azimuth
to half power \ elevation
Aerial power gain over iso¬
tropic source G . •
Receiver noise level <L,
416 m.
20 kw.
±8 6*
± 140*
60
6-7 x 10~ 14 watts
813 m.
30 kw.
±12“
±7“
25
1-3X10-" watts
813 m.
240 kw.
±12“
±6“
36-8
1-3 xltH* watts
8-20 m.
240 kw.
±12“
±12“
28
1-3 X10-“ watts
The 4-m. aerial system was steerable and was used at various azimuths
with the elevation fixed at 10°. The 8-m. aerial system was fixed to
t Almond, M.. Davies, J. G., and Lovell. A. C. B.. Observatory, 10 (1950), 112; Mon.
Not. Roy. Astr. Soe. Ill (1951). 685; 112 (1952), 21; 113 (1953), 411.
XII § , RADIO-ECHO RESULTS AND CONCLUSIONS
ssssssssrSSSiSSr-
Ls of ground reflections, the mean range of the ob8erv ®J
reduced. The net result was an improvement in sensitm y 1
mcnt IH to the extent of about 1-5 magnitudes in the b ® ltin S'" ag
of meteors detected (see § 1 (/))- The recordmg instrument «d th
method of determining velocities has been described m Chapter .
(6) Organization of Experiments OQQ ,. rA
‘ The basic purpose of the experiments, arrangements was »
the velocity distribution of sporadic meteors whose paths lay in th
great circle^plane through the apex of the earth’s way. The ^
reflection properties of meteor trails (see Chapter III p ^‘ e ^ 3
selection to be achieved partially with narrow-beam aerials or ented at
right angles to the plane through the apex. Actually, owing to the finite
wfdth ofthe aerial beams, the meteors recorded are those lying betwee
two smaU circle planes enclosing the great circle; the ^ckness of the
•sUce’ depending on the width of the beam. In order that the hourly
rates could be sufficiently large the apex experiments were eunedoiit
in the autumn mornings in the neighbourhood of 06h. when the apex of
the earth's way lies near its highest altitude, on a great circle plane
nassing approximately overhead and cutting the horizon in the north
and south. Similarly, 'antapex experiments’ were earned out during
the spring evenings in the neighbourhood of 18h. when the antapex of
the earth’s way occupies this position. Thus for all the experiments the
aerial beams were either fixed in an easterly direction or movable for a
small angle around it. Since for a given heliocentric velocity the geo¬
centric velocity depends on the elongation of the meteor radiant from
the apex of the earth’s way, it was possible with these arrangements to
obtain distributions for velocities in the neighbourhood of maximum
velocity (apex) and minimum velocity (antapex). These distributions
were then compared with the theoretical distribution to be expected it
all the meteors were moving at the parabolic velocity limit so that an
appreciable hyperbolic component would be immediately apparent.
The following specific experiments were made:
(i) Equipment I was used in the early morning hours between 1948
September 18 and December 18, with a certain amount of aerial
214
THE VELOCITY OF SPORADIC METEORS—V XII, §1
movement in order to keep the apex on the circle of echo. The
230-5 hours of observation yielded 67 velocities which are plotted
in Fig. 100.
(ii) Equipment II was used in the early morning hours between 1949
October 10 and December 20 with the aerial fixed at azimuth 90°.
In 43-5 hours of observation 187 velocities were measured as
shown in Fig. 101.
(iii) Equipment II was used between 17h. and 19h. from 1950
February 18 to April 29 with the aerial fixed at azimuth 90°. The
213 hours of observation yielded 87 velocities which are plotted
in Fig. 102.
(iv) Equipment III was used in the early morning hours between 1950
November 8 and December 14 with the aerial fixed at azimuth 90°.
In 10-7 hours of observation 335 velocities were measured as shown
in Fig. 103.
(v) Equipment III was used between 17h. and 19h. from 1951 March
29 to May 18 with the aerial fixed at azimuth 90°. The 56-5 hours
of observation yielded 57 velocities which are plotted in Fig. 104.
(vi) Equipment IV was used in the early morning hours between 1951
November 18 and December 6 with the aerial fixed at azimuth
90°. The 21 hours of observation yielded 362 velocities which are
plotted in Fig. 105.
(c) Experimental Errors
In order to provide a standard of comparison and a basis for the
estimation of errors, equipment II was also employed to measure the
velocities of the Geminid meteors in 1949 December. The measured
velocity distribution is shown in Fig. 106. In 05h. 48m. 122 velocities
were measured, giving a mean of 35-9 km./sec. and a standard deviation
of 4-6 km./sec. The errors of the individual velocity measurements can
be estimated from the diffraction photographs. The effect of errors in
range measurement is small, and it is found that the error depends
principally on the number of echo pulses between the maxima and
minima, and on the number of Fresnel zones observable. In deriving the
individual errors in these Geminid velocities it was assumed that the
position of each maximum or minimum could be estimated to ± 1 pulse.
The r.m.s. value of the error for the 122 individual velocities calculated
on this basis was 2-4 km./sec. This value is considerably less than the
standard deviation of the histogram in Fig. 106. This discrepancy could
arise either because the basis of error estimation is wrong or because of
25
Velocity l hm/eec-t
Flo . ,00. The l ? e “ U, ® < * I V ^°^^ n d ^^8) Uti 'ni» h lJi2re^cttl^di*tribution*o»l|
:S« dStti 2S Z shown as a smooth curve, and is norma.ized
to the equivalent number of observations.
IBS**'
fss.rrrx
Velocity {hm/soc)
"■ ,ci '
LTnTl (g) ^ii) P The theoretical distribution calculated as dwcnbed m the
Lt isshol as a smooth curve, and is normalized to the equivalent number of
observations.
s* 5-
O IO 20 30 40 SO 60
Velocity (km/sec)
Pi O’ 102 - The measured velocity distribution (histogram) for the first antapex
experiment (equipment II, spring 1950). The unshaded parts are referred to
m § 1 ( g) (iii). The theoretical distribution calculated as described in the
text is shown as a smooth curve, and is normalized to the equivalent number
of observations.
160
20 30 40 SO 60 70 60
Velocity (km/sec.)
Fxo. 103. The measured velocity distribution (histogram) for the third apex
experiment (equipment III, autumn 1950). The unshaded parts are referred to
§ 1 ( g) (iii). The theoretical distribution calculated as described in the text
shown os a smooth curve, and is normalized to the equivalent number of
observations.
Fio. 104. The measured velocity distribution (histogram) for the second
antapex experiment (equipment III, spring 1951). The unshaded parts are re¬
ferred to in § 1 (?) (iii). Tho theoretical distribution calculated as described
in the text is shown as a smooth curvo, and is normalized to the oquivalont
number of observations.
160
°0 20 30 40 SO 60 70 BO
Velocity (km/sec.)
Fio. 105. The measured velocity distribution (histogram) for the fourth apox
experiment (equipment IV, autumn 1951). The unshaded parts are referred
to in § 1 ( g ) (iii). The theoretical distribution calculated as described in the
text is shown as a smooth curve, and is normalized to tho equivalent number
of observations.
218
THE VELOCITY OF SPORADIC METEORS—V XII, §1
the existence of an actual spread in the Geminid velocities. The matter
was investigated as follows.
In the largest group of homogeneous velocities between 34 and 38
km./sec. (Fig. 106), N meteors were selected on which the average
number of independent measurements of velocity per meteor was greater
Fio. 106. The velocity distribution for the Geminid meteor shower measured
during the period 0-16 Dec. 1949, with equipment II for the purpose of assess¬
ment of errors in the velocity measurements.
than three. Let the mean velocity of the nth meteor be v n , and the
separate measurements of its velocity be v nR , v nb , etc. Let the average
number of measurements of velocity per meteor be I\ Then, if we write
Ana = v n -v na , the quantity
Vnt (1)
is a measure of the accuracy of a single measurement, the sum being
taken over the NT measurements made. The mean standard deviation
of each meteor velocity is then
2 A*
7 :
Nr(r-i)
A sample of sixteen Geminid meteors was selected which yielded
XII, §1 RADIO-ECHO RESULTS AND CONCLUSIONS 219
fifty-seven individual velocity measurements, giving T — 3 56. The
value of (1) is then 1-75 km./sec., and the mean error in the velocity o
meteor for the group M km./sec.
An alternative method of estimating the individual errors from th
group result has been described by Davies.f Let v represent the true
velocity of the meteor, and v lf v a two independent measures of its
velocity. If the mean velocity of the group, v', is known accurately then
errors of measurement and § 2 can be defined by
?! - V-Vj,
?2 =
The true deviation x = v'—v
and the observed deviations
Xl = v'-vj, x 2 = v'-v 2 .
Since = v'— v +?i = *+5i
2 (XjX 2 ) = 2 ( x +?i)( x +? 2 )
= J x 2 (since and ? 2 are uncorrelated).
If the standard deviation of the observed velocities is a and of the
true velocities a x then y ~ 2 /ft ,
2*' , _Xi t ,2I*
or "N -- N + N ’
where x' is the mean of the measured deviations x x> x 2 .
T . liq IV..I** 2 M
Thus N - N N
Thus
In a group of fifty-six meteors, with two measures of velocity for each,
2 x ' a waa 20-1 and ^ was 17-5. This represents a measured devia-
N N
tion a' = 4-5 km./sec. and a true deviation o x = 4-2 km./sec. The errors
of measurement are then given by (2) as 1*6 km./sec.
In view of the different number of velocity measures in the two
methods the discrepancy between the first figure of M km./sec. and the
second figure of 1 - 6 km./sec. is reasonable, and a final value of 1*4 km./sec.
was adopted as the standard deviation in a velocity of 35 km./sec. The
value of 2-4 km./sec. estimated from the errors in the zone spacing is
therefore too great, and it appears that the zone maxima and minima
can be estimated to better than ± 1 pulse.
f Davies, J. G., unpublished (Ph.D. thesis, Manchester, 1952).
220
THE VELOCITY OF SPORADIC METEORS—V XII, § 1
For the work on the sporadic distribution it is necessary to find this
error for other velocities. If the fractional error in estimating a zone
length is constant, the error should be proportional to the velocity. At
higher velocities more zones are measured and the error therefore
increases less rapidly. Consequently the adopted values of the errors
given in Table 70 have been based on the empirical formula Av oc Vv,
the proportionality being fitted to the point at 35 km./seo.
Table 70
Adopted Values of Errors in the Velocity Measurements
v km./sec. 20 30 40 50 60 70
Av km./seo. 1 06 1-29 1*50 1-67 1-83 1-98
A check on these values at v = 60 km./sec. has been applied by using
the first method described above on a sample of forty-three sporadic
meteors with velocities between 58 and 61 km./sec. measured in 1950
November and December. These yielded 172 independent velocity
measurements and gave the standard deviation as 1-3 km./sec. Scaling
as above to achieve the mean of the first and second methods gives a
value to be adopted of 1*7 km./sec., in agreement with Table 70.
The mean range of the Geminid measurements was 400 km. and the
wave-length 8 m. In cases where R and A differ, the errors have to be
adjusted in proportion to ^/(RA).
These error values were applied to the theoretical distributions
calculated as described in the next section, in order to produce the
distributions with which the experimental results could be directly
compared.
(d) The Theoretical Velocity Distribution
The theoretical velocity distributions appropriate to the above
experimental conditions have been calculated by Clegg.t As a basis for
the comparison it was assumed that all sporadic meteors moved in
parabolic orbits, and approached the earth from random heliocentric
directions. The radiant concentration and velocity are then expressed
as functions of the elongation from the apex of the earth’s way. The
actual velocity distribution observed from such a distribution depends
on the directional characteristics of the aerial system. The main features
of the calculation will be described in this section.
(i) Calculation of the radiants and geocentric velocities. In Fig. 107 a
meteor is approaching the earth O from heliocentric direction X at
t Clegg, J. A., Mon. Not. Roy. Astr. Soc. 112 (1952), 399.
XII 51 RADIO-ECHO RESULTS AND CONCLUSIONS 221
elongation « 0 from the ape,. Its geocentric direction will be Y, and the
elongation € will be given by
sine = (A 0 sine 0 )(l+AS+ 2 ^o COS€ o) »
where An = V/V B , V being the hehocentric velocity of the m ® teor ^
t l oAM 2 U» earth. The geoeentrio r.loerty of the
meteor v can be written as AV e , where
A = (AS—l+cos*«)*+eosc. w
■Apex
If the density of meteors near the earth is 4.N per km * then the
number approaching per second from hehocentric directions between
e 0 and e 0 + d€ o be XT *v • a
2ttNAV e sin e 0 d« 0
and the corresponding geocentric flight directions he between « and e+de,
concentrated within a solid angle 2w sin ede. .
The number whose radiants he within a small solid angle dfi at elonga-
tion c is therefore
which, using (3) and (4), becomes
N, _ 2A«V e (5)
N _ A„(AS+A*-1)‘
These formulae neglect the effect of the earth’s gravitational attraction.
For the present purpose the modification to (5) can be neglected but the
true geocentric velocity v g from (4) becomes
v* = A*V|+2r e g, ( 6 >
where r e is the radius of the earth and g the acceleration due to gravity.
222
THE VELOCITY OF SPORADIC METEORS—V XII, §1
In the present case the calculations have been made for meteors
moving in parabolic orbits (A 0 = V2). Fig. 108 shows the values of v
and N e /N for this case, plotted as functions of c for V E = 29-8 km./sec.
Fxo. 108. N,/N and v, plotted as functions of c, for meteors approaching
tho earth from random heliocentric directions, with parabolic velocities.
(ii) The directional characteristics of the aerial. The beamed aerial
used in the experiments described above is represented in Fig. 109, which
shows the celestial sphere drawn for the observing station at 0. The cone
aOb represents the limits of the main lobe of the aerial beam. Since the
reflection from the meteor trails is specular, the apparatus recorded only
those meteors whose radiants lay in the strip of sky enclosed by the
small circle arcs xzy, x'z'y', lying symmetrically about the great semi¬
circle Sz 0 N which has X as its pole, where OX is the axis of the aerial
beam. The measurements were restricted to the times when either the
apex, or antapex, A, was crossing this strip.
To find the relative numbers of meteors of different velocities which
enter the aerial coverage, the strip can be divided into a number of
elementary segments, in the way indicated by the dotted lines. If these
are sufficiently small, the meteors emanating from any one will have the
XII, § 1 RADIO-ECHO RESULTS AND CONCLUSIONS 223
game velocity and direction of flight, and they can be treated aa mcmbera
of a single shower with a point radiant situated m the centre of the
seement The elongations of the centre points of the segments from
"?Tl„™d,7na .h. ™lu„ of v, .Od NJN found tom «» oun,..
in Fig- 108.
Each of the apex and antapex experiments referred to above extended
over several months, and in computing N,/N and v e mean values were
taken for the declination of A. Observations were made over periods
of approximately 2 hours, during which A moved some distance across
the strip via the path pq, and a mean position was assumed. It was
found sufficient to divide the strip xzy, x'zy, into forty-five segments
of equal area, in the way shown in the figure. The elongation « of the
centre point of each segment from the apex, and the altitude and azimuth
relative to the direction OE was measured by constructing a model of
Fig. 109 on a sphere.
(iii) The effective collecting area of the apparatus. The probabilities of
detection of meteors by the apparatus will differ for the various segments
in Fig. 109, and in order to determine the relationship between the true
hourly numbers of meteors from the various segments, and the corre¬
sponding radio-echo rates, the effective collecting area of the apparatus
must be found for the individual radiant positions. This effective area
has already been discussed in Chapter IV for meteors of a single shower.
For the individual segments in Fig. 109 the treatment given by Cleggj
is as follows.
f Clegg, J. A., Mon. Not. Roy. Astr. Soc. 112 (1952), 399.
224
THE VELOCITY OF SPORADIC METEORS—V XII, §1
The echoes from the meteors emanating from a single segment are all
returned from the neighbourhood of a plane surface perpendicular to
the direction of the radiant and passing through O. In Fig. 110 the
radiant is in the direction OR, at altitude fS. OABC is the earth’s surface
and the echo plane OXYA is inclined at (90°—/3) to the horizontal. The
Fio. 110. Sensitivity contours on the echo plane. Oa, Ob represent the limit*
of the aerial coverage. The shaded area xwyz represents the collecting area of
the apparatus for meteors of a given mass group.
aerial polar diagram is represented, as in Chapter IV, by contours on
this plane corresponding to different values q 0 >Qi>*« of the overall
sensitivity of the apparatus. Then for a trail whose reflecting point lies
on the contour q p the amplitude Z of the echo is given by equation (3)
of Chapter IV, Z = kq p a„, (7)
where k is a constant depending on the parameters of the apparatus, and
<x 0 is the electron line density in the trail.f It is convenient to choose
the q values such that q p+1 = yq p , where y is a numerical factor greater
than unity, determined by the required contour spacing. A geometrical
method for constructing the contours for a given aerial system and any
f It is assumed that the electrons behave as individual scatterers: that is, equation
(6) of Chap. Ill applies. In the magnitude range covered by the series of experi¬
ments this assumption is justifiable. For more densely ionizing meteors the quantity
in (7) could not be assumed to be the line density (see Chap. HI) and the collecting
areas derived here would need modification.
XII, §1 RADIO-ECHO RESULTS AND CONCLUSIONS
radiant position is described by Cleggt in an appendix to the original
P Consider meteors of a certain mass group which produce their maxi-
mum electron density corresponding to at height mm , and assume
that they are just detectable out to points xy, on the contour q 0
(Fig. 110). Meteors of the same mass which cross the echo plane closer
to the axis of the beam cut contours of higher value and will be detectable
above and below mm'. A curve xwyz can be defined inside of which
meteors of this class can be observed. Similar areas can be defined or
meteors in other mass groups with values of a 0 differing from a 0 by factors
y ± p, where p is an integer. The conditions determining the shapes of these
areas are discussed below. Experimentally it is found that there is a
fairly well-defined range limit beyond which no echoes appear, and the
largest area which need be considered corresponds to this limit. The value
of a 0 = aj 1 corresponding to this area can be found from the parameters
of the apparatus.
The number of meteors falling on the earth from the 1-th segment with
electron density values between a<, and aj,-f da^ can be written as
dN.41 = Vi F (“o) d <*i, (®)
where F(c*i) is a predetermined function, and
+«$)**• (9)
AS being the area of the segment. ^ ^
A series of curves similar to xwyz, corresponding to a$\ —,... can
be constructed for any radiant position, and their areas a 0t a v ...o p
measured. The number n of such curves will be finite, the smallest having
an area a n _ lt the area a D corresponding to oc J7y n being zero. Consider
the trails between a™ and aJ7y; the largest will be detected in the area a 0 ,
but the smallest only in a v The effective collecting area for this group
is therefore approximately equal to £( fl o+°i) and the total hourly number
detected will be
a-/y
FK) d a4.
Similar expressions follow for other groups and the total echo rate Nj for
3595.68
t Clegg, J. A., Mon. Not. Roy. Astr. Soc. 112 (1952), 399.
Q
220
THE VELOCITY OF SPORADIC METEORS—V XII, §1
meteors from the 1-th segment will therefore be
n
Ni = hl K-1+flp) J *«)d«i. (10)
p “° «rh*
Hence, if F(«i) is known, and if the collecting areas can be constructed,
a relationship can be found between and the observed hourly rate.
Fio. 111. Theoretical curve for the variation of ionization
a* of a meteor with height h. The maximum ionization a£
occurs at height h«.
The shapes and sizes of the collecting areas depend on the variation of
electron density along the trail. Clegg used the relationship derived by
Herlofsonf for the relation between the electron density a 0 and the
height h in the atmosphere:
where a J, is the maximum ionization used above, h 0 is the height of maxi¬
mum ionization, and H is the scale height. In this aj, is given by
oi oc mf(v)sin/?, (12)
where m is the meteor mass, v the initial velocity, and p the altitude of
the radiant. In the present case the dependence of h 0 on m, v, and p has
not been taken into account, since the errors introduced thereby in
computing the field of view of the apparatus are small. The value of
ajcxo as a function of (h—h 0 ) for H = 10 km. is plotted in Fig. 111.
This curve can be used directly to find the overall collecting area of
the apparatus for any given radiant position. Consider, for example, the
delineation of the area xwyz of Fig. 110. A plan of the echo plane, show¬
ing the configuration of the sensitivity contours is first constructed, and
f Herlofson, N., Rep. Phyt. Soc. Prog. Phye. 11 (1947), 444.
XII, § 1 RADIO-ECHO RESULTS AND CONCLUSIONS 227
the position of the line mm', corresponding to the height of maximum
ionization, is estimated. The area extends laterally to the points x,y,
where this line cuts the contour q 0 , and its boundary cuts the inner
contours at points where the electron density has fallen by successive
multiples of the chosen factor y. The vertical distances of these points
above and below mm' can be read off from Fig. 111. To find the corre¬
sponding distances along the echo plane, which is inclined at an angle
P to the vertical, we must multiply by sec p. Corresponding areas for
meteors of other mass groups can be drawn in a similar manner.
As an example, the collecting areas for the aerial system used in equip¬
ment II (§ 1(a)), corresponding to the various segments of Fig. 109,
are given in Table 71.
Table 71
Collecting Areas of Aerial System
0
deg.
Collecting areas in km*.
X
deg.
q, - 2-07
q, - 1 44
q« - i-oo
q, - 0 69
q, = 0-48
q,-0-34
q 0 - 0-23
S3-5
10
386
1 350
3 800
MEM
6 460
oo O
Q2
10
645
1 820
2 900
wtzl
8 050
aii
100
10
65
965
1 830
2 990
■WE™
7 080
* vv
xr,
20
370
1 450
2 580
3 540
7 250
oo
935
20
645
1 770
3 310
4 760
6 120
7 020
9 170
102-5
20
166
677
1 925
)3&- gil.' jfll
4 180
6 320
6 830
86-5
30
• •
1 350
2 680
4 030
5 320
6 920
Qrt
30
680
2 160
3 640
4 990
5 630
7 730
9 170
30
322
1 060
2 060
3 280
4 180
5 320
6 650
88
40
370
1 930
3 600
6 310
7 670
98-5
40
805
2 250
3 600
5 220
6 920
8 370
9 660
109-5
40
129
1 130
2 090
3 150
4 180
5 410
6 700
90
50
• •
• •
1 290
3 220
6 480
7 570
102
60
900
2 250
3 700
5 960
7 610
9 350
11 920
116
50
• •
935
1 770
2 740
3 860
6 320
6 510
91-5
60
• •
• •
• •
• •
645
2 570
5 800
108
60
645
2 540
4 570
6 770
9 180
10 950
13 350
126
60
481
1 450
2 800
3 770
5 080
6 450
7 950
94
70
• •
..
• •
..
• •
• •
• •
119
70
805
3 000
5 800
8 220
10 700
13 700
16 730
164
70
• •
741
2 090
3 280
4 770
5 800
7 410
100-5
80
..
• •
• •
• •
• •
• •
180
80
805
3 220
8 050
11 300
14 500
19 300
23 400
The two left-hand columns indicate the azimuth x and the altitude P
of the centre points of the segments relative to the axis of the aerial
beam. Other columns show the measured areas for values of the limiting
sensitivity contour differing by factors of q = 1-44. It was found
experimentally that the most distant meteors detected by the apparatus
228
THE VELOCITY OF SPORADIC METEORS—V XII, §1
had their reflecting points on the contour q 0 = 0-23, and the largest
area in each case has been taken as the one extending outwards to this
contour. Of the total of forty-five segments, all except the one nearest
to the zenith were situated symmetrically in pairs, on either side of the
axis of the beam, so that only twenty-three radiant positions were
required.
(iv) Calculation of the velocity distribution. The collecting areas of
Table 71 can be used to find the numbers of meteors from each segment
detected by the apparatus, provided the functions F(ai) and f(v)sin0
of (8) and (12) are known. F(<*i) depends on the mass distribution of the
meteors, and, on the basis of the evidence given in Chapter VII, F(«i) has
been taken as l/cxj,. Equation (10) then gives the number of meteors Nj
from the 1-th segment as
N, = i^logy 2 ( a P - 1 + fl p)’ < 13 )
p-i
As regards the function f(v), Clegg showed that the internal evidence
from the experiments suggested that f(v) = v a with a»l.f
It may be assumed, therefore, that the meteors detected out to the
farthest contour q 0 = 0-23 were those of such a velocity and radiant
altitude that vsin/3 had its maximum value (vsin0) m . In the apex
experiments this condition was fulfilled for particles emanating from the
segment at an altitude of 70°, while for the antapex experiment the
corresponding altitude was 35°. In the case of a segment for which
vsin/3 is lower than the maximum value by a factor y p , where p is a
positive integer, the outermost collecting area must be taken as the one
extending outwards to the contour q p = 0-23 y p . For segments for
which v sin does not differ from (v sin/?) m by an integral power of y the
areas can be estimated by interpolation. After correcting the figures of
Table 71 in this way for each radiant position in turn, the appropriate
values of £ (0 p _i+a p ) can be found for the various segments. Since tj
is knownfrom (9), the relative values of N t can be determined from (13)
and, using (4), can be plotted as a function of velocity.
Examples of the theoretical velocity distributions obtained in this
manner are shown in Fig. 112 (a) and (6).
t This value, derived from the experimental results, is not in agreement with the
value calculated by Opik (Tartu Obs. PM. 30 (1940). no. 5) of « = 2-5. The assumption
of a higher value for a shifts the peaks of the theoretical distributions m ^g. il2 to
higher velocities. It will be seen in § 1 (*) that such an assumption woifid serve
to strengthen further the deductions made from the experiments A va^ue of j < 1
would shift the maximum of the curves in Fig. 112 to lower velocities. However, it is
not possible to justify on theoretical grounds values of a < 1.
XII, §1 RADIO-ECHO
RESULTS AND CONCLUSIONS
229
Fio. 112. The theoretical velocity distributions calculated
for equipment II (§ 1 (a)).
(а) The distribution for the 1949 apex oxperimont.
(б) The distribution for the 1950 untapex experiment.
(«) Comparison of the Theoretical and Experimental Distributions
The theoretical distributions for the various equipments and experi¬
ments described in §§ 1 (a) and (6) were calculated as described
above. In order to obtain convenient curves with which the various
experimental distributions could be compared, the errors of measure¬
ment, assessed as described in § 1 (c), were superimposed on the
theoretical distributions. For each 1 km./sec. interval the proportion of
meteors which would remain in the interval or be shifted 1 , 2 ,3,etc.,
km./sec. either side was calculated. Summation of the numbers in each
interval then gave the final distribution for comparison with the experi¬
mentally observed distribution. These error-corrected theoretical curves
230
THE VELOCITY OF SPORADIC METEORS—V XII, §1
are shown as the full lines together with the histograms of the experi¬
mental distributions in Figs. 100-5. A discussion of these curves is
given in § 1 fa).
(/) The Range in Magnitudes of the Measured Meteors
Two methods were used to investigate the range of equivalent visual
magnitudes covered in this work on the sporadic distribution. The first
method involved the calculation of the electron densities in the trails
and a subsequent conversion to visual magnitude, while the second
method involved a comparison of the radio echo and visual meteor rates.
(i) The electron densities and conversion to visual magnitudes. The rela¬
tion between the electron densities in the meteor trails, the parameters
of the apparatus, and the signal strength of the radio echo has been dis¬
cussed in Chapter III. It was found that the meteors investigated with
the equipments described in § 1 (a) produced electron line densities,
oq, such that equation (6) of Chapter III could be used without signifi¬
cant error. For each equipment the wave-length A and transmitter power
P are known. For each meteor the range R is measured, and the received
power di can be calculated from the measured signal noise ratio of the
radio echo. In the case of the remaining parameter—the power gain of
the aerial G—the value to be used is not that quoted in § 1 (a) for
the main axis of the aerial, but the value which is effective in the direction
of the observed echo. This depends on the range R, and azimuth from the
axis of the aerial. The azimuth for the individual echo is not known, but
a method of calculating the most probable value of the sensitivity
(G/R*) for each case has been described by Almond, Davies, and Lovell.t
Hence the individual electron densities can be calculated from equation
(6) of Chapter HI. The data are summarized in Table 72 for the various
apex and antapex experiments.
The conversion of these line densities to equivalent visual magnitudes
requires a knowledge of the ionizing efficiency of meteors. In reviewing
the subject in 1948, HerlofsonJ concluded that the ionizing efficiency was
0 01 (the probability that an evaporated meteor atom will produce an
electron by collision), and on this basis a meteor of visual magnitude -f 1
should produce 10 12 electrons/cm. path. Although the early radio-echo
results appeared to support this estimate, a better understanding of the
radio-wave scattering processes (Chap. Ill) soon made it apparent
that this estimate of the ionizing efficiency must be too low by a large
f Almond, M., Daviee, J. G., and Lovell, A. C. B., Mon. Not. Roy. Aetr. Soc. Ill
(1951), 685.
X Herlofson, N., Rep. Phya. Soc. Progr. Phya. 11 (1948), 444.
XII, § 1
RADIO-ECHO RESULTS AND CONCLUSIONS
Table 72
Distribution of Electron Densities observed in the Experiments on the
Velocity Distribution
231
Line density,
a 0 . electrons/
cm.xlO"
398-031
261-398
169-251
100-169
631-100
39-8-63 1
25 1-39-8
16-9-25-1
10-9-16-9
631-100
3-98-0-31
2-61-3-98
1-69-2-61
Zenithal
Number of meteors in the various a
:perxments
magnitude
ra, calcu¬
lated from
a 0 using
eg. (14)
Equipment
I
1948
Apex
Equipment
II
1949
Apex
Equipment
II
1960
Antapex
Equipment
III
1950
Apex
Equipment
III
1951
Antapex
Equipment
IV
1961
Apex
3-6-30
1
4
*»
0 •
1
# 0
0 •
• •
0 •
4-0-3-5
4-6-40
60-4-6
6-6-60
60-6-6
6-9-80
2
7
12
26
16
• •
2
20
37
81
24
<9
6
17
20
26
4
4
3
4
10
65
114
0 0
0 0
0 0
2
4
7
# •
• •
0 •
• •
1
16
70-0-6
4
12
0 •
117
13
31
7-6-70
•.
• •
• •
11
6
160
80-7-5
• •
• •
0 0
* *
1
2
08
8-6-80
• •
• •
• •
2
24
90-8-6
9-6*90
• •
• 0
0 0
0 0
0 0
• #
1
factor The work of Greenhow and Hawkinst on this subject has been
referred to in Chapter III, from which it appears that the most reasonable
value to assume for the ionizing efficiency is 0-2, at least for values of
„ < jo 13 electrons/cm. path. On the basis of the results for the Perseid
meteor shower, the relation between zenithal magnitude m and «„ is
given as m = 35—2-5loga 0 . ( 14 )
Since the major number of velocities in the experiments described above
were of the same order as the Perseid velocities (60 km./sec.), tins rela
tion has been used to obtain the visual magnitudes for the line densities
listed in Table 72. _ , *
(ii) Magnitude estimates from comparison of the visual and radio-echo
rates. An alternative method of estimating the range of magnitudes
covered in these experiments consists in a comparison of the rates
observed visually and by the radio-echo apparatus. This comparison
can be made if the relative collecting areas for meteors of different
magnitudes are known both for the visual observer and for the radio¬
echo equipment. The case of the visual observations has been discussed
in Chapter II, and the relevant data for the number of meteors of different
magnitudes seen by a visual observer is contained in Table 4 (p..10).
The calculation of the collecting area for the radio apparatus follows
+ Greenhow, J. S., and Hawkins, G. S., Nature, 170 (1952), 355.
232
THE VELOCITY OF SPORADIC METEORS—V XII, §1
that described in § 1 (d) (iii) above. Assuming a mean position of 45°
for the apex during the course of the experiments, the relative numbers
of meteors passing through a square kilometre of the 95 km. surface
from a square degree in different parts of the sky is first calculated.
The total of these numbers is then normalized to the appropriate number
in column 5 of Table 4 (p. 10), and hence the true number of meteors
falling on a square kilometre of horizontal surface from a given area of
sky is obtained. The number of meteors of given magnitude observed by
the radio apparatus is obtained by summing the product of the number
from a given area of sky and the collecting area of the aerial for that
magnitude and radiant direction, the sum being taken over all parts of
the sky to which the aerial is sensitive. The subsequent procedure of
comparison between the visual and radio data may be illustrated by
reference to the 1950 apex experiment.
On the above basis the magnitude distribution peaked at + 5-7 and
the hourly rate was 2-1 for an assumed visual rate of one per hour (accord¬
ing to the normalization carried out against Table 4). At 06h. in the
autumn mornings the true visual rate is 10 per hour. Thus the above
radio rate has to be increased to 21 for the assumed magnitude distribu¬
tion. The true magnitude range is then obtained from a comparison of
this figure with the actual radio-echo rate. The observed rate was 292
per hour, and hence the assumed magnitude scale must be shifted by
2-5 log(292/21) or 2-9 magnitudes, giving a magnitude distribution with
maximum at (5-7-f-2-9) = 8-6. Actually in this experiment only 40
per cent, of the echoes could be classed as ‘velocity type’; the majority of
the remainder were long-duration echoes having been recorded by the
apparatus after trail distortion. On this basis the above scaling is modi¬
fied to magnitude 7-6 at the peak of the distribution.
Similar analysis was applied to the 1949 and 1951 apex experiments;
the results are given in Table 73 compared with the magnitude estimates
for the electron density calculations. The method could not be applied
satisfactorily to the antapex experiments owing to lack of data on the
correct visual rate to be assumed.
In view of the uncertainties regarding the ionizing and luminous
efficiencies of meteors on the one hand, and the uncertainty regarding
the collecting area of a visual observer for meteors of a given magnitude
on the other, the agreement between the two estimates must be regarded
as very reasonable.
The final assessment of the numbers of meteors in the various magni¬
tude groups observed during the apex experiments is given in Table 74.
XII, §1 RADIO-ECHO RESULTS AND CONCLUSIONS
Table 73
Comparison of Magnitudes obtained from Visual Rates and Electron
Densities
From visual rate
(:magnitude at peak
frequency)
From electron density
(:magnitude at peak
frequency)
+
+
1949 apex .
00
5-5
1950 apex
7-5
70
1951 apox
8-5
8-0
Table 74
Number of Meteors observed in Different Magnitude Groups during the
Radio-echo Apex Experiments
Magnitude]
m
Electron line
density a # X 10‘°
1948
apex
1949
apex
1950
apex
1951
apex
Total
3 and 4
> 100
9
29
8
40
6
39-8 -100
37
118
14
M
109
0
15-9 - 39-8
20
30
109
MM
232
7
0-31 — 15-9
• •
• •
128
mm
315
8
2-51— 031
• •
• •
1
KJ
94
(g) Discussion of Results
A comparison of the experimental and theoretical distributions in
Figs. 100-5 shows immediately that the results are in serious conflict
with the measurements of Opik, and that if any meteors move with
hyperbolic velocities they must represent only a small fraction of the
total number. Nevertheless, the experimental distributions show con¬
siderable disagreement when compared with the theoretical distributions
calculated on the basis of a random distribution of parabolic orbits.
The significance of these departures is discussed in this section.
(i) The apex experiments. The theoretical distributions calculated on
the basis of parabolic orbits show that the most probable velocity should
be nearly 72 km./sec., whereas in each case the observed distribution
peaks at about 60 km./sec. The possibility of instrumental causes for
this cut-off has been excluded by measurements on a wave-length of 8 m.
f Group 5 denotes magnitudes 5 0-5-9 inclusive, and similarly for the other groups.
234
THE VELOCITY OF SPORADIC METEORS—V XII, §1
(equipments II, HI, IV) as well as 4 m. (equipment I), and also by the
observed antapex distribution. Deceleration can also be eliminated,
since the radio-echo velocity measurements on the shower meteors
(Chap. XIH et. seq.) show that this effect is small. The low value of
the peak velocity therefore appears to be a real effect.
The two possible sources of the discrepancy lie in the basic assumptions
from which the theoretical curves were derived. Firstly, it was assumed
that the parabolic orbits were distributed at random. The apparatus
was sensitive to radiants contained in a strip of sky cutting the ecliptic at
the apex and continuing along a line of constant ecliptic longitude from
this point. But the area which would produce velocities of 60 km./sec.
from meteors moving at parabolic heliocentric velocity lies near the
zenith, 45° from the apex and in ecliptic latitude 45°. Hence, if the
results are to be explained in this way, a very large concentration of
radiants would be required in this area. Such a concentration is com¬
pletely at variance with the visual and radio-echo results on the distribu¬
tion described in Chapter VI. Secondly, it was assumed that the meteors
were moving in parabolic orbits. On this basis and the assumption of
random directions, over half the meteors come from the zone of sky close
enough to the apex to yield velocities between 67 and 73 km./sec. Any
reduction in the heliocentric velocity will increase the concentration in
this area. Thus the observed distributions give a measure of the helio¬
centric velocity distribution, which may be estimated by subtracting the
earth’s orbital velocity from the observed velocity peak. Hence the
results are compatible with sporadic meteors moving with a heliocentric
velocity of about 34 km./sec., that is, in elliptical orbits with periods of
about two years. The complete observational disagreement between
these conclusions and those of Opik is extremely pronounced.
(ii) The antapex experiments. The early results, especially those
obtained with equipment I, were criticized by Opikf on the grounds that
the apparatus possessed an instrumental cut-off which precluded the
measurement of high velocities. The antapex experiments were primarily
designed to answer this criticism, and the distributions in Figs. 102,104
show that the lack of high velocities is a real effect. The discrepancy
between the observational and theoretical curves is similar to that
observed in the apex experiments. On account of the broad shape of
the distribution it is difficult to analyse the cause of the discrepancy in
any detail, although general support is given to the conclusions reached
in (i) above.
f Opik, E. J., Irish AstT. J. 1 (1950), 80.
XII. §1 RADIO-ECHO RESULTS AND CONCLUSIONS
(iii) The effect of side lobes. Each of the aerial systems had a subsidiary
lobe at high elevation in an easterly direction. Although the power
radiated in this lobe was small, meteors recorded in it were at short
range, and hence the sensitivity was relatively high. The meteors thus
recorded were distinguished by their short range, and their contributions
in the histograms of Figs. 101,102,103,104, and 105 are unshaded^ lhe
most probable radiant point for these meteors is low in the west, that is,
near the antihelion point in the apex experiment, and near the hehon
point in the antapex experiment. The exact elongation is not known, but
estimates based on the most probable elongation indicate that the velo¬
cities of these meteors are also non-hyperbolic. The theoretical curves
have been normalized to distributions which omit these short-range
meteors, since they do not arise from the parts of the sky considered in
deriving the theoretical distribution.
(iv) The high velocity tail. In the apex experiments 860 meteors were
measured in the main lobes of the aerials. Seven of these yielded velocities
exceeding 80 km./sec. Although this is less than 1 per cent, of the total, it
is interesting to examine whether this actually represents a hyperbolic
component, or whether the high velocities can be attributed to errors of
measurement. The details of the seven measurements are listed in
Table 76.
Table 75
Details of Seven Velocities in excess of 80 km./sec.
Date
Time
d. h. m.
Velocity
km./sec.
Range
km.
Amplitude
X receiver
noise level
Electron density
X 10 l0 /cm. path
1948 Nov. .
2 09 33
80-6 ± 2-9
276
7
29
1949 Nov. .
2 06 12
83-3 ± 6-9
380
6
30
1949 Nov. .
12 06 50
82-4± 6 0
700
6
136
1949 Nov. .
19 05 40
96-9±12-6
616
9
119
1949 Dec. .
10 06 26
87 0± 9-6
460
7
42
1950 Nov. .
18 05 21
80-4± 81
700
6
26-8
1951 Nov. .
26 07 10
83-5±lll
180
9
4-9
The errors quoted are calculated from the number of pulses in each
zone, and although this yields a high value for the error (see § 1 (c)),
the figures can be compared directly with those obtained in other
velocity ranges. The corresponding errors for meteors in the velocity
group 65-75 km./sec. measured in the same experiments are given in
Table 76.
236 THE VELOCITY OF SPORADIC METEORS—V XII, §1
Table 76
Mean Errors of Velocity Measurement at 70 km./sec.
Experiment ( apex)
1948
1949
1950
1951
Total
No. of meteors
11
43
36
62
152
R.m.s. error km./sec. .
3-5
6-5
4-3
4-3
4-6
The r.m.8. error of the seven velocities in Table 76 is 8-6 km./sec., and
when compared with the r.m.s. error of the 70-km. group in Table 76 it
is evident that the seven meteors have unusually large errors, and that
to 40 60 60 no to 40 60 60 too
(C). Magnitude 7. 322meteors if). Magnitude 6. 93 meteors
Velocity (km/sec )
Fxo. 113. The velocity distribution (a) for all magnitudes of meteors in the
apex experiments, (6) for magnitude groups 3 and 4, (c) for magnitude group
6, (d) for magnitude group 6, (e) for magnitude group 7, (/) for magnitude
group 8.
their true velocities may lie within the parabolic limit. Even so, it can
be shown on statistical grounds that the number is more than would be
expected, and, although the number is too small for any definite con¬
clusion to be reached, the fact cannot be excluded that about 1 per cent.
237
XII> §1 RADIO-ECHO RESULTS AND CONCLUSIONS
of the meteors observed in the apex experiments may have had velocities
in excess of the parabolic limit. It is possible, of course, that a result
this nature may be due to planetary perturbations.
(v) Effect of meteor magnitude on the velocity distribution. The sample
of 860 meteors measured in the main lobe of the aerial systems during the
apex experiments has been tested for any change m velocity distnbu-
tL with magnitude. The results are given in Fig. 113 («H/>. .bom ^
it is clear that no significant change occurs in the velocity distribution
over a range of five magnitudes.
2. McKinley’s measurements of meteor velocities
Simultaneously with the work described in § 1 above, McKinleyt
carried out a series of measurements in Ottawa using the continuous-
wave technique for measuring velocities (see Chap. IV). The transmitter
generated 1-6 kw. on a wave-length of 10-0 m. The aerial consisted of a
half-wave dipole, mounted a quarter wave-length above pound, giving
a broad beam. The receiving system was located 7-5 km. distant from the
transmitter and used a similar aerial. A separate pulsed transmitter
and receiver were used for measuring the meteor ranges. The method ot
recording the meteor velocities, giving a continuous envelope of the
Fresnel diffraction pattern, instead of the discontinuous envelope of the
pulse system, has been described in Chapter IV. McKinley’s arrange¬
ment is sharply distinguished from the arrangement used by Almond,
Davies, and Lovell in the aerial system. Whereas the aerial system
described in § 1 was highly selective, McKinley’s system is effectively
non-selective, and records meteors independently of their direction of
approach, apart from a small region in the neighbourhood of the zenith.
(a) Details of Observations
The velocity data were collected over 15 months from 1948 December
to 1950 March. The equipment was operated for at least one 48-hour
period per month in order to accumulate observational data over an
entire calendar year. By this means McKinley collected 10,933 echoes
of good quality suitable for velocity analysis. Velocity distributions of
the total number observed in each operating period are given in Fig. 114,
with the numbers normalized for comparison. Fig. 114 (1) shows the
distribution for all measured velocities. The trend to higher velocities
in the autumn months is well marked, and the influence of the pronounced
showers-Geminidst Figs. 114 (2) and (16); Perseids§ Fig. 114 (11); and
t McKinley, D. W. R., Aslrophys. J. 113 (1951), 225.
X See Chap. XV.
§ See Chap. XIV.
238 THE VELOCITY OF SPORADIC METEORS—V XII, § 2
Total
moeaois.w
Mar 26 6 SO. 1949
~ Apr 20 - 22 J 949 I
%w.w 9 ~\
N= 10.931
t
N = 72
A*
N — 611
it
N = SS 7
■ -
IM
o 40 eo
' 1 'Jo' 1 Vo
1 ■ 1 • 1 ■ 1 13
40 go
40 e
( 1 )
( 2 )
( 3 )
( 4 )
(S)
“ July 7-9. 194 9 I
M = 299
July H U. 1949
Ns 939
M
iL
Ja
A
~L
0 40 BO
■ 1 ' 1 ■ 1 ' 1
40 90
* ' “ 1 'g'o
n *T n -Jo
PT « T i 3
(6) (7) (8) (9> (10)
so
Aug 11-14.19*9
Aug T2P4.1949
r Upt >9 21.1949 I
" Oct 20 22.1949
’ Not IS'17,1949
to
Nm 1.040
N =■ 1.107
Nml79
N=S09
%
10
jJl
J9ik
0
(
> 40 90
(U)
40 90
(12)
■ 1 V 1
(13)
■ • ' j 0 ' 1 ■ a i Q
(14)
40 9t
(IS)
Fio. 114. Tho velocity distributions measured by McKinley from 1948 Dec. to 1960
March. The histograms represent the total distributions for the periods indicatod,
usually covering from 48 to 72 hours continuously.
Ordinates: per cent, of total in period (all histograms are normalized).
Abscissae: velocity in km./sec.
the summer day-time streams - ) - Fig. 114 (6)—(10)—is also evident. Pre¬
paratory to the statistical analysis of these observations, McKinley made
a detailed examination of the Geminid shower in order to investigate
the errors in the analysis and to deduce a probability function of general
application.
(6) Analysis of the Geminid Shower Velocities
The hourly distribution of velocities from 17h. to 12h. E.S.T. for
the three nights 1948 December 10-13 covering the maximum of the
f See Chap. XVIII.
Fin 116 The hourly distribution of velocities measured by McKinley between 17h. and
12h. E.S.T. on 1948 Dec. 10-13.
Ordinates: per cent, of total measured in hourly intervals (all histograms are
normalized).
Abscissae: velocity in km./sec.
Geminid shower is shown in Fig. 115. In these graphs the data for the
corresponding hour of each of the three nights have been added. Near
transit of the radiant (around 02h. E.S.T.), when the radiant was high
in the sky, the ranges were beyond those recorded by the apparatus.f
The velocity group between 30 and 40 km./sec. has been analysed further
into unit steps and is shown in Fig. 116 for both the 1948 and 1949
Geminid showers. These distributions must contain meteors which do
not arise from the Geminid radiant; but by comparison with other
+ The variation in range of the recorded echoes with radiant altitude arises because
of the specular reflection property of the trails and has been discussed in Chap. IV.
240 THE VELOCITY OF SPORADIC METEORS—V XII, §2
periods it can be shown that the proportion of non-Geminids is unlikely
to exceed 15 or 20 per cent, of the total. The mean velocities from
Fig. 116 are
1948 851 meteora 35-2 km./sec.
1949 234 „ 35-5
Mean 35-25 „
These velocities are mean apparent observed velocities and require the
following corrections to obtain the geocentric velocity.
50 5/ 32 33 34 35 36 37 36 39 40
Observed velocity (km/sec.)
Fio. 116. The velocity distribution of probable Gcminid meteors as measured
by McKinley: (a) in 1948 Dec. 851 observations, mean velocity 35-2 km./sec.
(6) in 1949 Dec. 234 observations, mean velocity 35-5 km./sec.
(i) Correction for diurnal motion. Fig. 117 shows the diurnal-motion
correction for Ottawa, and also the average correction which should be
applied to the observed velocities each hour to allow for the separation
of the receiver and transmitter. The resulting net correction, which is
also shown in Fig. 117, when averaged over the observational period,
amounts to —0 036 km./sec. McKinley therefore adopts 35-2 km./sec.
as the observed velocity corrected for diurnal motion.
(ii) Correction for deceleration and zenithal attraction. In order to
correct for deceleration, McKinley assumes that the average mass of the
meteors is about 1 milligram, and that the average zenith distance of
origin is 50°. Using equations deduced by Whipple,f he then derives
t Whipple, F. L., Rev. Mod. Phya. 15 (1943), 243.
XII, §2
241
RADIO-ECHO RESULTS AND CONCLUSIONS
the mean deceleration to be —2-5 km./sec. 2 and V = 36 0 km./sec. The
finally corrected value v g for the geocentric velocity is then obtained
from equation (6) (p. 221). This gives v g = 34-2 km./sec., which is in
reasonable agreement with Whipple’sf value of 34-7 km./sec., derived
from photographio measurements.
Fio. 117. (a) . Diurnal motion correction for Geminid meteors.
-Statistical correction for avorago position of Geminid meteors due to
spacing of transmitter and recoivor. - Net correction to be applied to
obsorvod velocities. (6) Observed hourly rates of probablo Geminid meteors
(1948 data).
McKinley next deduces a relation between the radio meteor rates and
zenith angle of the radiant from the information given in Fig. 117 (6).
The transit time of the radiant was 02h. 10m. E.S.T. The meteor numbers
for corresponding times on either side of transit were summed and
plotted against zenith angle of the radiant yielding the full-line curve of
Fig. 118. The ordinate P(z) represents the probability that the radio
system will detect a meteor when the radiant is at a given zenith distance.
This function is then used in the analysis of the sporadic distribution.
Also given in Fig. 118 is P(z) = cos z which represents to a first order the
probability function for a visual observer.
3595.68
t See Chap. XV.
R
242
THE VELOCITY OF SPORADIC METEORS—V XII, §2
Fio. 118. The probability function P(z) for McKinley's observations.
- Empirical radio probability.
-Theoretical visual probability.
Fio. 119. Diagram for calculation of theoretical velocity distribution
in McKinley's experiment.
(c) The Theoretical Velocity Distribution
The theoretical velocity distribution applicable to the measurements
made by McKinley can be derived in the following way, assuming that
the meteor radiants are uniformly distributed. In Fig. 119 the observer
is at 0, and the apex is at elevation <f> relative to the observer’s horizon, or
at a distance a from the observer’s zenith. Small circles on the celestial
sphere labelled V and v g are drawn such that a true radiant on the V
circle will appear, owing to the earth’s motion, to lie on the v g circle. If
243
XII, §2 RADIO-ECHO RESULTS AND CONCLUSIONS
v g and V are the geocentric and heliocentric velocities respectively, the
appropriate transformations are
v^ = V 2 -f 900+60V cos b,
Vg sin c = V sin b.
Owing to the earth’s attraction, the meteor will appear with an apparent
velocity v, and a correction Az to the zenith angle z of the radiant will
be required, given by y2 _ y2 +125>
Az v—v K . z
tan — =-- tan
2 v+v g 2
V may be regarded as a parameter, and selected values assigned to
all the radiants over the celestial sphere. Table 77 then shows typical
values of v, c, and Az for uniform values of b and for three values of the
parameter V.
Table 77
Typical Transformations for McKinley's Velocity Distribution
V = 30
V- 36
V - 42
b
V
c
Az
v
c
Az
B
o
Az
0°
6103
0°
0° 58'
6694
0°
0° 48'
72-86
o°
0°
41'
16
60-51
7-5
1
0
66-39
8-2
0
50
72-27
8-8
0
42
30
59-02
16-0
1
2
64-75
■ 4+1
0
52
70-50
171
0
44
46
56-55
22-5
1
8
62-04
0
67
67-61
26-5
0
48
60
5315
30-0
1
18
58-32
33-0
1
4
63 63
35-5
0
54
75
48-90
37-6
1
32
53-66
41-5
1
16
58-67
44-8
1
4
90
43-88
45-0
1
56
48-18
60-2
1
35
62-81
64-5
1
19
105
38-20
52-5
2
34
41-98
69-2
2
6
46-22
64-8
1
44
120
32-02
60-0
3
44
3523
68-9
3
2
39-11
76-1
2
27
135
25-53
67-5
6
4
28-18
79-8
4
55
31-73
■ 11
3
48
160
19-14
75-0
11
54
21-22
93-8
9
16
24-63
106-9
6
35
165
13 65
82-5
30
20
15-32
117 4
21
18
18-84
134-2
12
22
180
11-18
90-0
90
0
12-69
180-0
39
24
16-40
180-0
17
36
The correction Az only becomes serious for meteors with low heliocentric
velocities with radiants near the ant apex. It has therefore been neglected
by McKinley in deriving the theoretical velocity distribution. The con¬
version of the V radiants to the v radiants could be achieved by means
of a surface integral over the sphere, including the probability function
P(z); but a simplified method of numerical integration was preferred
according to the following procedure:
(i) For a selected value of a, uniform density of radiants may be
represented by uniform and equal line density along each of the
V circles at equal increments of b. The V circles are divided into
244 THE VELOCITY OF SPORADIC METEORS—V XII, §2
equal angular elements so that the transformation of points on
the V circles to the v g circles can be effected by drawing great
circles through the apex at equal intervals of the angle Z. The
number of radiants selected on the V circle then has to be multi¬
plied by sinb.
(ii) The distance z is computed for each point on the v g circles selected
by 10° increments of the angle Z, by means of the spherical
triangle defined by the apex, zenith, and the selected point.
(iii) Each point on the v g circle is now multiplied by the P(z) function
corresponding to the zenith distance of the point according to
Fig. 118.
(iv) The sum of the modified densities on the v g circle is then the rate
of meteors of velocity v g which will be detected by the radio
system for the particular values of a and V selected in (i). As an
example, the curves in Fig. 120 are the theoretical distributions
for elevation of apex <f> = +45°, 0°, —45°, and for V = 42, 36,
30 km./sec. in each case.
(i d) Comparison of the Observational Data with the Theoretical Distributions
The appropriate observational data for comparison with the theoreti¬
cal curves such as those of Fig. 120 were selected by first determining the
local times corresponding to the particular values of <f> for each of the
operating periods. Only a limited amount of the total information can
be used in these comparisons—for example, <f> reaches -j-45° only from
June to December, and —45° only from December to June. Moreover,
the observing hours in which the strong major showers occurred were
necessarily rejected. The histograms in Fig. 122 show the observational
data for the selected values of <f> = +45°, 0°, and —45°. An attempt was
then made to fit these curves by a synthesis of the various theoretical
distributions. None of the possible combinations yielded a satisfactory
fit, the closest approach being obtained by synthesizing equal numbers
of 36 and 42 km./sec. meteors but with few 30 km./sec. meteors.
McKinley therefore investigated the alternative assumption of a
non-uniform radiant distribution, assuming first that there were more
direct than retrograde orbits (that is the inclinations of the orbits
favoured the interval 0°±90°), and that the ellipticities were large-
more nearly parabolic than circular.
In the analytical method, described in (c) above, these conditions
were implied by postulating more radiants with b > 90° than with b < 90°
(the parameter b is a measure of the combined effect of inclination and
XII. §2 RADIO-ECHO RESULTS AND CONCLUSIONS
4>—4S 0
/ 7 '
VS. 1 A » - ** “
Velocity I km/sec)
Fio. 120. Theoretical velocity attributions for elevation of apex
4 _ +45°. 0°, -45°.
_ V = 42 km./sec.-V - 36 km./sec.V = 30 km./soc.
ellipticity) and by eliminating V = 30 km./sec., which removes the very
elliptical orbits. The adopted density distribution for this case, com¬
pared with the previously assumed uniform case is shown in Tig. 12 .
The densities on the V circles in (c) are then modified according to this
SO' 60' 90'
True distance from apex (b)
Fio. 121. Assumed theoretical distribution of radiants
as a function of distance from the apex (6).
_Uniform distribution. - Adopted non-uniform distribution.
distribution and the numerical integration repeated as in (c). The final
theoretical curves are shown in Fig. 122, assuming equal numbers of
V = 36 and 42 km./sec. meteors but none of V = 30 km./sec.
(e) Discussion
Examination of Fig. 122 shows a reasonably good agreement between
the theoretical and observed distributions; except that in the case of
</>=-{- 45 the number of high velocities exceeds those predicted. It is
possible to change the density distribution of Fig. 121 to obtain a better
fit by increasing the radiants in the region b = 0°-30°. Other reasons
for the discrepancy may be that faster meteors produce relatively more
ionization and hence more are detectable in the high-velocity range.
McKinley points out that so many variable parameters are involved
in deriving the theoretical curves in (c) that it is possible to fit the data
from very dissimilar theoretical postulates. It is clear, however, that
none of the 10,000 meteors studied by McKinley can be definitely asserted
240
THE VELOCITY OF SPORADIC METEORS—V
XII, § 2
Flo. 122. Observed and theoretical velocity distributions in McKinley’s
experiment for elevation of apex 4 = +45°, 0°, —46°.
“ - Observed distribution.-Theoretical, assuming equal numbers
V = 36 and 42 km./sec., no 30 km./sec., and the non-uniform distribution of
Fig. 121.Theoretical visual curves on the same assumption.
All curves normalized to the observed distribution for <f> => 0°.
to have originated in interstellar space. In fact there are thirty-two
meteors (0-3 per cent.) in the interval 75-79 km./sec.; but if these were
interstellar it is difficult to see why an appreciable number was not found
with velocities greater than 80 km./sec. It seems preferable to regard
this small hyperbolic component aa due to interplanetary meteors which
have suffered perturbations. In any case there is no indication whatso¬
ever of the preponderance of hyperbolic velocities found by Opik and
Hoffmeister (Chaps. IX and VI).
As regards the equivalent visual magnitudes of the meteors, McKinley
does not enter into a detailed analysis. From a comparison of the visual
and radio-echo rates he considers that the average meteor studied
probably had a magnitude of 4-4 or 4-5, with a limiting magnitude of
4-7 or 4-8. This range of magnitudes is comparable with that covered
in the work of Almond, Davies, and Lovell (see § 1).
3. General conclusions on the velocity of sporadic meteors
During the last twenty-five years a large fraction of the work in
meteor astronomy has been concerned with the problem of the origin
of the sporadic meteor component. In the period between the two
world wars the investigations of Hoffmeister and Opik led to the belief
that most of the sporadic meteors had an origin in interstellar space and
travelled with markedly hyperbolic velocities in the solar system. Then
the precise photographic measurements failed to show such high
velocities; on the contrary, the surprising result was obtained that some
247
XU, §3 RADIO-ECHO RESULTS AND CONCLUSIONS
of the sporadic meteors moved in very short period orbits. J he an ^
of the British visual meteor data aiso faded to show the artwat££
very high velocities. Criticism and counter-onticism effectively
Tunpasse, but since 1948 the new radio-echo techniques have been
applied to this problem and have yielded results which are opposed to
the hyperbolic theory. Neither in the British nor in the Canadian wor
is there any indication of the high velocities demanded m th ® c ° n °! U8 '°"
of Hoffmeister and Opik. Hoffmeistert has concluded that his own
observations can be interpreted in the light of the new results, but Opiir.I
even in the face of the new results, does not move from his belief in tne
hyperbolio theory.
The complication of Opik’s results and his analysis are evident lrom
Chapter IX, and now that the non-hyperbolic theory is widely accepted
the task of explaining his conclusions remains. If the validity of the
basic observational data is accepted, there remains only the question of
the validity of the statistical analysis which has already been queried by
Olivier § At any moment there is a wide spread in the velocity distribu¬
tion of sporadic meteors and the distribution itself is asymmetrical. It
does not seem impossible that the application of conventional stellar
statistics to such a problem may lead to erroneous results, but no one
has yet attempted the task of such a quantitative investigation of Opik s
results.
Hence, although Opik’s results remain an enigma, the contemporary
conclusions to be drawn from the surveys of the previous chapters is that
only a small percentage, if any, of the sporadic meteors are moving with
hyperbolic velocities; and that the few cases of small hyperbolic velocities
which probably exist more likely arise from planetary perturbations
than from the interstellar origin of the meteors.
t Hoffmoister, C. # private communication.
% Opik, E. J., Irish Astr. J., loc. cit.
§ Olivier, C. P., Pop • Astron. 46 (1938), 325.
XIII
THE MAJOR METEOR SHOWERS-I
THE PERMANENT STREAMS OF JANUARY TO JUNE
1. Introduction
The major meteor showers are the dominant observational events in
meteor astronomy. They occur when the earth sweeps through con¬
centrations of debris in space. About a dozen major showers have been
recorded visually and several recur annually, indicating that the debris
is itself moving in an orbit around the sun. After a few days the earth
generally moves out of the debris; hence, although the showers can be a
spectacular occurrence, their contribution to the total number of meteors
entering the atmosphere is somewhat less than the sporadic meteor
contribution.
The meteors in a given stream travel in roughly parallel paths in the
earth’s atmosphere. Their apparent point or area of divergence is the
radiant position. By convention, the shower takes its name from
the constellation, or star, near which this position lies. If the radiant
position and the velocity of the meteors in the earth’s atmosphere are
known, the orbit of the stream can be computed as described in Chapter
V. The available information about the major showers varies a great
deal. For some, the orbits are known with precision, and the association
of the debris with other constituent bodies in the solar system has been
established.
In many cases the showers are observed every year with about the
same intensity, indicating that the debris is fairly uniformly dispersed
around the orbit. For purposes of classification we shall refer to these
as permanent streams. In others the debris is localized in the orbit and
the streams exhibit a marked periodicity (Chap. XVI). In one or two
cases major meteor streams have completely vanished (Chap. XVII).
Finally, the radio-echo techniques have revealed the existence of intense
meteor streams active in the summer day-time. These are discussed in
Chapter XVIII.
Table 78 summarizes the major showers which are dealt with here.
These all give displays (or have done in the past) with visual hourly
rates exceeding 20 to 50. In addition to the showers listed there are a
number of minor streams occurring at various times during the year
with rates of only a few per hour. For example, the great catalogue of
OF JANUARY TO JUNE
249
XIII, § 1
PERMANENT STREAMS
Table 78
The Major Meteor Streams
Shower
Quadrantids
Lyrids
ij-Aquarids .
Pons-Winnecke
8-Aquarids .
Summer day-time streams
Persoids
Giacobinids
Orionids
Taurida
Leonids
Bielida
Geminids
Uraida
Date of maximum
Jan. 3
April 21
May 4-6
Juno 28
July 28
May, June, July
Aug. 10-14
Oct. 10
Oct. 20-23
Nov. 3-10
Nov. 16-17
Nov.-Dee.
Dec. 12-13
Dec. 22
Classification and chapter^
Permanent Chap. XIII
Lost
Permanent
Permanent
Permanent
Periodic
Permanent
**
Periodic
Lost
Permanent
Chap. XVII
Chap. XTV
and Periodic
Chap. XVIII
Chap. XIV
Chap. XVI
Chap. XV
Chap. XV
Chap. XVI
Chap. XVII
Chap. XV
Chap. XV
Denningf published in 1899 lists 4,367 radiants, and the modem com¬
pilations of HoffmeisterJ and Opik§ give attention to many more
streams than those listed in Table 78. However, the showers described
in the present book are those which are widely recognized as bemg of a
major character, and for which information is available from a variety
of sources.
2. The Qiiadrantid shower
(a) History
The Quadrantid shower is one of the most intense showers at present
active. It is short-lived and the sharp maximum occurs over a period of
a few hours between January 2-4. Fisher|| has given the complete
history of this shower and collected the known data up to 1927. It is
named after an obsolete constellation Quadrans Muralis found in early
nineteenth-century star atlases—located at the junction of the areas of
Draco, Hercules, and Bootes. The occurrence of the shower has not been
traced back for any considerable time. In 1861 Wartmanntt recognized
the period January 2-3 to be a noteworthy one from his observations
since 1853. QueteletJt claims first publication in 1839. Herrick§§ also
t Denning, W. F., Mem. Roy. Astr. Soc. 53 (1899), 203.
X Hoffmeister, C., Meteorstrdme (Weimar, 1948).
§ Opik, E. J., Circ. Haro. Coll. Obs. (1934), no. 388.
|| Fisher, W. J., ibid. (1930), no. 346.
•ft Wartmann, Bull. Ac. R. Brux. 8 (2) (1841), 226.
JJ Quotelet, A., Catalogue des principales apparitions d'ttoiles filantes, 1839.
§§ Herrick, E. C., Amer. J. Set. {II), 39 (1840), 334.
260 THE MAJOR METEOR SHOWERS—I XIII, §2
published the same suggestion at about this time. Since 1860 there are
records of fairly regular observations of the shower, mainly by observers
in the British Isles. These have been hindered greatly by the poor
weather conditions of early January and the short life of the shower.
Since 1946, however, systematic observations have been made by the
radio-echo technique.
Fio. 123. The hourly rato of the Quadrantid metoor shower from observations
between 1860 and 1930 according to data collected by Fisher. The small
numbers by the plotted points are the dates in January to which the observa¬
tion refers.
(6) Activity
According to Fisher,f useful counts of the Quadrantid rate were made
only in 24 Januaries out of a possible 68 between 1860 and 1927. His
summary of the available information is given in Fig. 123. The greatest
maxima apparently occurred in 1864 (60 per hour); 1879 (> 42 per hour);
1897 (64 per hour); 1909 (180 per hour); 1922 (60 per hour). Information
on the activity of the shower is also given by PrenticeJ from 1921 to
1940. The maximum rate during this period appears to have occurred
in 1932 (80 per hour) although the results are influenced by unfavourable
weather. The hourly rate plotted against longitude of the sun over this
t Fisher, W. J., loc. cit.
X Prentice, J. P. M., J. Bril. Astr. Asa. 51 (1940), 19.
262 THE MAJOR METEOR SHOWERS—I XIII, §2
by Hawkins and Miss Almond, f The curve of activity against solar
longitude is given in Fig. 125 for the years 1951,1952,1953. This shows
good agreement with the curve given by Prentice (Fig. 124) for the
epoch of maximum and for the duration of the shower. The maximum
ratesj determined by the radio-echo apparatus are given in Table 79.
Table 79
Maximum Rates of the Quadrantid Shower determined by the Radio-echo
Apparatus
Date
Solar longitude
Maximum hourly rate
©
1947 Jan. 3
282-6
34
1948 Jan. 4
283-0
76
1949 Jan. 3
282-5
41
1950 Jan. 3
282-6
70
1951 Jan. 3
282-1
90
1952 Jan. 4
282-8
104
1953 Jan. 3
282-6
170
There is no evidence from these various data of any marked periodicity
in activity. This is contrary to earlier views since Denning and Mrs.
Wilson§ considered that the Quadrantids might have a period of 13J
years. Also, from the maxima between 1860 and 1927 Fisher|| considered
that a mean cycle of 14-6 years was indicated. On this basis another
maximum would be expected in 1936; but Prenticeff gives a rate of only
35 for that year, whereas he considers the return of 1932 (80 per hour) to
have been very rich. The more reliable radio-echo data (Table 79) as
yet gives no support to the idea of any periodicity. The activity in 1953
appears to have been the greatest recorded for over forty years.
(c) Radiants
According to Fisher,|| Stillman Masterman first determined the
Quadrantid radiant in 1863 as a 238°, 8 +46° 26'. In 1864 Herschel
obtained a value of a 234-0°, 8 +50-9°. Many subsequent determinations
showed similar discrepancies. The various determinations up to 1927
have been collected by Fisher and are plotted in Fig. 126 for singly
observed meteors and in Fig. 127 for doubly observed meteors. The
radiant points cluster around a 232°, 8 -f 52° but are widely scattered.
t Hawkins, G. S., and Almond, M., Mon. Not. Roy. Astr. Soc. 112 (1952), 219. Except
the information for 1952-3 which is unpublished.
X The parameters of the radio apparatus were adjusted so that the hourly rates
recorded corresponded to those seen by a visual observer under good sky conditions.
This applies to all the radio-echo rates quoted in Chapters XEQ-XVHI.
§ Denning, W. F., and Wilson, F., Mon. Not. Roy. Astr. Soc. 78 (1918), 198.
|| Fisher, W. J., loc. cit.
ft Prentice, J. P. M., loc. cit.
253
XII! §2 PERMANENT STREAMS OF JANUARY TO JUNE
During the night of 1929 January *-3. Fisher and Miss Olmstedf recorded
three Quadrantid meteors photographically. Their final value
mean radiant was a 231-8°, 8 +48-3°. All subsequent observations h
Fio. 126. Radiant positions of tho Quadrantid shower
(plotted on great circle chart) as given by Fisher for
F singly observed moteors between 1860 and 1927.
2SO 240 250
Fio. 127. Radiant posit ; ons of the Quadrantid
shower (plotted on great circle chart) as given by
Fisher for doubly observed meteors between 1860
and 1927.
confirmed that the Quadrantid radiant is spread over a wide area.
Prentice* remarks that the radiant is exceedingly complex and appar¬
ently covers a wide area at least 20° in diameter with centre about
a 230°, 8 4-50°. The spread in radiant position has been confirmed by
t Fisher, W. J., and Olmsted, M., Circ. Harv. Coll. Obs. (1930), no. 347.
♦ Prentice, J. P. M., loc. cit.
264
THE MAJOR METEOR SHOWERS—I XIII, §2
the radio-echo observations as seen from Table 80 which gives the
coordinates for the showers of 1950, 1951t and 1952, 19534
Table 80
Radiant Coordinates for the Quadrantid Shower determined by the
Radio-echo Technique
Date
Solar longitude
0
Radiant coordinates
Radiant diameter
deg.
a (deg.)
8 (deg.)
1960 Jan.
1
280-6
233
+ 62
10
Jan.
3
282-6
231
+ 47
12
Dec.
28
276-9
224
+ 62
5
Dec.
30
2780
228
+ 46
5
1951 Jan.
1
280-0
231
+ 46
5
Jan.
2
2810
228
+ 61
8
Jan.
3
282-1
232
+ 49
< 3
Jan.
6
284-1
236
+ 51
4
Jan.
6
285-1
236
+ 60
10
Jan.
7
286-2
227
+ 49
6
1952 Jan.
2
280-8
227
+ 66
6
Jan.
3
281-8
233
+ 47
4
Jan.
4
282-8
233
+ 48
3
Jan.
6
283-9
224
+ 62
4
Jan.
6
284-9
232
+ 60
6
1953 Jan.
1
280-5
221
+ 60
8
Jan.
2
281-6
214
+ 47
10
Jan.
3
282-6
231
+ 60
6
Jan.
4
283-6
231
+ 46
7
(d) Velocities
Fisher? lists fourteen velocities determined from doubly observed
meteors between 1903 and 1918. The values range from 25-8 to 77-3
km./sec. with a mean of 41-8 km./sec. Omitting the four most widely
dispersed values, the mean reduces to 38-5 km./sec. There do not
appear to be any other published velocity determinations of Quadrantid
meteors until the advent of the radio-echo diffraction technique in 1948.
Then, on 1948 January 3 and 4, Ellyett and Davies|| measured 30 velo¬
cities, the distribution of which is shown in Fig. 128 (a). The low-velocity
group (mean 22-4 km./sec.) was obtained when a non-directional aerial
f Hawkins, G. S., and Almond, M., loc. cit.
X Jodrell Bank observations, unpublished.
§ Fisher, W. J., loc. cit.
|| Ellyett, C. D., and Davies, J. G., Nature, 161 (1948), 696; Davies, J. G., and
Ellyett, C. D., Phil. Mag. 40 (1949), 614.
XIII. §2 PERMANENT STREAMS OF JANUARY TO JUNE 2-5
system was in use at the beginning of the shower and is unlikely to '}*
associated with the Quadrantid radiant. The remaunng 25 velocities
give a mean of 371±3-5 km./sec. A further 37 velocities were measured
during the Quadrantid epoch of 1951 January and 25 velocities durrng
the epoch of 1952 January. The distribution for the 1951 measureme
which is shown in Fig. 128 (6). has a mean of 39-3±3-4 km./sec. T
Fia 128. The velocity distribution of the Quadrantid metoors moasurod by
the radio-echo diffraction technique, (a) January 1948. *^**1±Z+***•!**•
(neglecting the low-velocity group). (6) January 1951. Mean 39-3± 3-4 km./sec.
mean value for the complete 87 velocities (1948, 1951, 1952) is 39-6
km./sec. £ , .
Hawkins and Miss Almondf have investigated how much of this
velocity spread can be attributed to an actual spread in the heliocentric
velocity of the individual meteors in the stream. The standard deviation
of the observed geocentric distribution (a 0 ) can be written as
<*0 = oi + °R + a S +°A + °U’
where a E = standard deviation caused by random errors in the measur¬
ing technique;
o R = standard deviation resulting from the variation of apparent
elongation of radiant points;
o s = standard deviation introduced by sporadic meteors;
o. = standard deviation caused by differential atmospheric
deceleration;
o H = standard deviation introduced by a real spread in the
heliocentric velocities.
t Hawkins, G. S., and Almond, M., loc. cit.
266 THE MAJOR METEOR SHOWERS—I XIII, §2
o E may be obtained from the errors in the measurement of individual
velocities as described in § 1 (c), Chapter XII, a R from the observed
radiant positions and diameters, and o 8 from the measured background
rate of sporadic meteors. <j a can be estimated from the equations for
deceleration given by Whipple,f and hence o H can be estimated. For
the 1951 Quadrantid measurements Hawkins and Miss Almond obtain
o E = 1-0 km./sec., o a = 1-1 km./sec., o R = 1-7 km./sec., a A = 0-3
km./sec., and since o 0 = 3-4 km./sec., a H = 2-5 km./sec.
This result indicates that an actual spread in heliocentric velocities
may make a significant contribution to the dispersion of the velocities
in Fig. 128.
(e) Orbit
A preliminary attempt to define an orbit for the Quadrantid stream
was made in 1873 by Kirkwood ,% who, from qualitative observations,
derived a period of thirteen years. Fisher§ computed a heliocentric
velocity of 39-1 km./sec. for the Quadrantid meteors at the node, using
the mean radiant and velocity data compiled by him for the observations
up to 1927. He concludes that this result is not incompatible with the
heliocentric velocity of 41-8 km./sec. derived on the assumption of a
14-6 year period. Parabolic elements for the stream were computed in
1908 by Wenz|| and in 1913 by Davidsonft as given in Table 81.
Table 81
Parabolic Elements for the Quadrantids as computed by Wem, Davidson ,
and Hoffmeister , compared with Comet 1860 I
•
Epoch
Radiant
SI
deg.
i
deg.
n
deg.
q
a.u.
a (deg.)
5 (deg.)
Wenz
1908 Jan. 3d. 20h.
239
EE1
282-6
70-0
831
Davidson
1913 Jan. 2d.-3d.
232
282
72-8
96-2
0-981
Hoffmeister
19260
227 1
282-2
81-5
92-7
Comet 1860 I
• •
• •
mm
324-0
79-3
173-8
1*197
In commenting on this orbit Davidson points out that the motion is
direct, and that 1D25 days after perihelion the particles are at a distance
of 1 a.u., moving with a velocity of 41-6 km./sec. This leads to a geo¬
centric velocity in the earth’s atmosphere of 45-3 km./sec. Davidson
t Whipple, F. L., Rev. Mod. Phye. 15 (1943), 246.
t Kirkwood, D. f Proc. Amer. Phil. Soc. 13 (1873), 601.
§ Fisher, W. J., loc. cit.
|| Wenz, W., Bull, de la Soc. Astronom. de France, 22 (1908), 365.
tf Davidson, M., J. Brit. Astr. Am. 23 (1913), 233.
XIII, §2 PERMANENT STREAMS OF JANUARY TO JUNE 2ol
computes the width of the stream to be 1-BX 10* miles and states that
there is no corresponding comet. In 1919 Pokrovsky and Shame noticed
that the coordinates of the Quadrantids were nearly those ot Oomet
18601, which, like Biela’s comet, was remarkable because of its division
into two parts. Actually the epochs differ by a month and the association
does not seem very plausible. The comparison is given in Table 81.
Hoffmeisterf observed the Quadrantids in 1933 and considered that
there was evidence for a long-period orbit. The parabolic elements which
he computed are also given in Table 81. He was unable to find any
plausible cometary association.
The orbital elements computed by Hawkins and Miss Almond* trom
the radio-echo data are given in Table 82.
Table 82
Orbital Elements for the Quadrantids computed from the Radio-echo
and Photographic Data
SI {deg.)
co {deg.)
i {deg.)
o
q (a.u.)
a (a.u.)
/Quadrantids
Radio- I Quadrantids with
282-6±0-5
100±3
67 ± 2
0 44±003
0-97 ±004
i-7±01
ocho | decoloration cor-
V roction
282 6
166
67
0-46
0*97
1-8
O 4
Jacchia (photographic)
282-1
108
74
072
0 93
3*4
The limits of error were obtained from the estimated error of the
radiant determination and the probable error in the velocity distribu¬
tion. The coordinates were corrected for zenithal attraction and diurnal
aberration. The influence of the correction for deceleration (computed
according to the method and data given by Whipple§ and Jacchia||)
is shown separately in Table 82.
The orbit is of short period and high inclination and is therefore unlike
any known cometary orbits. The exceptional nature of the Quadrantid
orbit has since been confirmed by Jacchiatt who has calculated the
orbital elements from one doubly photographed meteor in 1951. This
information is also given in Table 82, and the two orbits are shown in
Fig. 129. The orbit intersects that of a near-parabolic comet (Comet
1939 a, Kozik-Pcltier) in two places at distances of 1*3 and 1-7 a.u. from
the sun, and the possibility of ejection of material (see Chap. XXI) at
either of these points to form the meteor stream has been considered.
t Hoffmcister, C., loc. cit. X Hawkins, G. S., and Almond, M., loc. cit.
§ Whipple, F. L., loc. cit.
|| Jacchia, L. G., Tech. Rep. Harv. Coll. Obs. (1948-9), nos. 2, 3, 4.
ft Jacchia, L. G., private communication.
S
3595.68
258
THE MAJOR METEOR SHOWERS—I XIII, §2
An ejection velocity of 20 km./sec. would be required and the idea does
not seem plausible. It must be concluded, therefore, that at present no
relation of the meteor stream with other bodies in the solar system can be
established.
V
• »
\ /
\ /
\ /
• •
i /
Fio. 129. Orbit of the Quadrantid stream calculated from the radio-echo
data (-) and the photographic data on one meteor (- --).
3. The Lyrid shower
(a) History
Although at the present time the Lyrid meteor shower gives only poor
displays, it is nevertheless renowned as a shower of considerable antiquity
which in the past has yielded displays of great intensity. Also, between
1800 and 1870 the calculations of Weiss,f Pape,J and Galle§ established
t Wei®, E., Asir. Nachr. 68 (1867), 382.
J Pape, C. F., ibid. 55 (1861), 206. § Galle, J. G. f ibid. 69 (1867), 33.
259
XIII, §3 PERMANENT STREAMS OF JANUARY TO JUNE
that a close similarity existed between the orbit of Comet 18611 and
that of the Lyrid meteors. In his work on the past history of the major
meteor showers, Newtont was able to trace the history of the Lynds lor
some 2,600 years. Some of these displays must have been very remarK-
able. Thus Olivierf quotes from Biot’s Chinese Catalogue : ‘March 2^
16 B.c.§ after the middle of the night, stars fell like a rain ; they were 10
to 20° long: this phenomenon was repeated continually. Before arriving
at the earth they were extinguished.’ The last great shower appears to
have been in 1803, when, according to contemporary newspaper accounts
collected by Herrick in 1839, an observer is stated to have counted 167
meteors in 15 minutes ‘and could not number them all’. It was about
this time that the work of Arago (1835), Benzenberg (1838, 1839), and
Herrick (1838, 1839) first confirmed the regular appearance of a shower
with its radiant in Lyra, around April 21, although the numbers observed
were small. Owing to the weak displays which have been given by this
shower during the past century, comparatively little accurate information
is available about it.
(b) Activity
Although it is inferred from some of the historical accounts mentioned
above that the Lyrid shower must have given great displays in the past,
its activity during the era of trained observers has been very low. For
example, the records of maximum activity as deduced from the observa¬
tions of the British Astronomical Association!! in 1884 and from 1893
to 1930, and of the radio-echo observationsft since 1947 are given in
Table 83. DenningtJ observed the stream carefully in 1884 since he
believed that Herrick’s idea of a 27-year period had some foundation.
The rate observed of 22 per hour is considerably higher than that found
subsequently, but later returns do not support the idea of the 27-year
period. Davidson§§ has given an account of the careful observations
under good conditions in 1912, but the rate was only 1 per hour.
It is, of course, likely that some of the visual observations represent
a lower limit owing to poor sky conditions or to the fact that the observa¬
tions may not have covered the period of maximum, but there is no other
t Nowton, H. A., Amir. J. Sci. (II), 36 (1863), 145; 37 (1864), 378.
$ Olivier, C. P., Meteors, ch. 6.
8 Corresponds to a.d. 1850 April 21.
II Mem. Brit. Astr. Ass. 1 (1892); 3 (1894); 4 (1895); 5 (1896); 6 (1897); 7 (1898);
8 (1899); 9 (1900); 10 (1901); 11 (1902); 12 (1903); 13 (1904); 14 (1905); 24 (1923);
32 (1936).
ft Hawkins, G. S., and Almond, M., loc. cit.
II Denning, W. F., Observatory, 7 (1884), 217.
§§ Davidson, M., J. Brit. Astr. Ass. 22 (1912), 364.
260
THE MAJOR METEOR SHOWERS—I XIII, §3
evidence of intense activity during this period except for the 1922 return.
Then on 1922 April 21a rate of more than 1 per minute appears to have
been recorded by observers in eastern Europe.t The British observers,
although working under good conditions, did not record this high rate,
but the accountj speaks of ‘very fine Lyrids* being observed with a
maximum at April 2Id. lOh. 45m.
Table 83
Maximum Hourly Rates of the Lyrid Meteor Shower
Year
Hourly rate
Year
!
I
1884
22
1922
3 to 100**
1893
6
1930
7
1895
6
1947
7
1896
Very low
1948
20
1898
6
1949
10
1899
Very low
1950
6
1901
8
1951
11
1903
4
1952
Very low
1912*
1
1953
7
• Davidson, loc. cit.
•• So© remarks in text.
In reviewing the work of the American Meteor Society for 1919-25
Prentice§ refers to this discrepancy and gives the comparison in Table
84 between the observations of H. N. Russell in Greece and his own
observations in Great Britain.
Table 84
The Lyrid Shower of 1922
Hourly raU in Hourly rale in
Hale Great Britain Greece
1922 April 20 0 6
1922 April 21 3 96
He concludes that the rich portion of the shower must be extremely
narrow. Nothing is yet known about the question of periodicity in the
Lyrid shower. Comet 18611, with which the shower is associated, has
a period of 415 years, but the historical data are insufficient to check if
there is any related periodicity in the shower. Although the hourly
rates are low, the epoch of maximum is shown to be sharp from the visual
observations of 1901|| and 1922ff for which published data are available
t Pop. Astron. 31 (1923), 172. J Afem. Brit. Astr. Ass. 24 (pt. iii) (1923).
§ Prentice, J. P. M., J. Brit. Astr. Ass. 40 (1930), 136.
|| Mem. Brit. Astr. Ass. 11 (pt. i) (1902). ft Ibid. 24 (pt. iii) (1923).
XIII, §3 PERMANENT STREAMS OF JANUARY TO JUNE
over several succeeding nights. The data plotted in Fig. 130 show a sharp
maximum on April 21 on both occasions.
Fio. 130. Epoch of Lyrid maximum as given by the visual observations
of 1901 and 1922. (The number by each plotted point gives the numbor
of meteors observed.)
Table 85
1/ijrid Radiants
Date
Radiant
No. of meteors
Observers
1922 April 21-76
a
deg.
2700
a
deg.
+ 32-6
17
U.S.A.
1922 April 21
271
+ 34
7 +
G.B.
„ 21
271
+ 33
4 +
»•
1928 „ 21
272
+ 33
4
•»
„ 21
272
+ 33-25
11
*•
1923 „ 20-85
280
+ 37-1
28
U.S.A.
1922 „ 21-82
280-2
+ 37-4
5-13
99
1923 „ 23-8
281-6
+ 35-6
19
9t
(c) Radiant
The first radiant coordinates for the Lyrid shower appear to have been
given by Herrick as a 273°, S +45°, 1839 April 18. Denningt states that
f Tanning, W. F., Mon. Not. Roy. Astr. Soc. 84 (1923), 46.
262
THE MAJOR METEOR SHOWERS—I
XIII, §3
he obtained convincing evidence for the motion of the Lyrid radiant in
1885, and in 1923 gave an ephemeris showing a movement from a 269°,
8 +33° on April 18 to a 278°, 8 +33° on April 26. Subsequently, a large
number of radiant positions were determined by visual observers, but no
precise agreement as to the coordinates has been reached. For example,
Prentice t compares group Lyrid radiants determined by reliable observers
in U.S.A. and G.B. as in Table 85.
Prentice concludes that such discrepancies cannot be due solely to
errors of observation and that the Lyrid shower must have double or
multiple centres. The most recent visual data on the radiant are those
given by Prentice! for the 1930 and 1931 returns as follows:
1930 April 21, a = 273-0°, 8 = +31-5°, diameter 1-8° (10 meteors).
1931 April 22, a = 272°, 8 = +32-5°, diameter 2-5° (4 meteors).
There is no published record of subsequent radiant determinations, but,
in the most recent summaries, Prentice§ lists the Lyrids as centred on
a = 271°, 8 = +31° with multiple centres.
The radiant coordinates given by the radio-echo technique|| are listed
as a = 273°, 8 = +30°, with a mean radiant diameter of 8°, but owing to
the low hourly rate more weight must be attached to the visual observa¬
tions.
(d) Velocities
The data on the velocity of Lyrid meteors are meagre. For example,
since 1895 only six velocity determinations, visually determined, are
given in the published records of the British observers as follows: 30,
48, 53, 61, 62, 64 km./sec. The scatter is so great that the values are
worthless. Three radio-echo determinations have been given by Millman
and McKinley,ft one by McKinley,!! and three by Ellyett§§ as listed in
Table 86.
The velocity of one Lyrid meteor, photographically determined by
the double-camera technique, has been listed by Jacchia.|||| It is Harvard
no. 1065, photographed on 1941 April 23-32 with velocities of 48-47
km./sec. at 87-5 km. altitude and 48-00 km./sec. at 80-0 km. altitude.
t Prentice, J. P. M., J. Brit. Astr. Ass. 40 (1930), 136.
X Prentice, J. P. M., Mem. Brit. Astr. Ass. 32 (pt. i) (1936).
§ Prentice, J. P. M., Brit. Astr. Ass. Handbook, 1947-50.
|| Hawkins, G. S., and Almond, M. p loc. cit.
tt Millman, P. M., and McKinley, D. W. R., J. Roy. Astr. Soc. Can. 42 (1948), 121.
XX McKinley, D. W. R.. J. Appl. Phys. 22 (1951), 202.
§§ Ellyott, C. D., unpublished (Ph.D. thesis, Manchester, 1948).
HU Jacchia, L. G., Tech. Rep. Harv. Coll. Obs. (1948), no. 2 (Harvard Reprint Series
11-26).
XIII, §3 PERMANENT STREAMS OF JANUARY TO JUNE
Table 86
Radio-echo Determinations of the Velocity of Lyrid Meteors
Date
Velocity
km./sec.
Reference
1948 April 21
48 |
48 >
Millman and McKinleyt
it a
*» *»
604:3 J
1948 April 22
47 04:2 0 -j
46-64:30 ^
4614:0 4 J
Ellyettt
1949 April 21
49 0 (beginning)
43-4 (end)
| McKinleyt
^As Mentioned in (a) above, the close rektionship between the Lyrid
shower and Comet 1861 I was established through the work of Weiss
Pape and GaUe in 1867. The elements of the comet’s orbit are giv
in Table 87, with the elements of the Lyrid orbit as originaUy computed
by Galle.t together with the mean Lyrid orb,t as derived from the
contemporary radiant and velocity data presented m (c) and (<*)•
Table 87
Orbital Elements for Comet 1861 I and the Lyrid Meteor Shower
Epoch
Radiant
ft
Ui
i
o
q
Velocity
{geocentric)
Period
{yearn)
Comot 18611
• •
• •
deg.
30-3
deg.
213-4
deg.
79-8
0-9835
a.u.
0-9270
km./sec.
48
415
Guile's Lyrid
orbit
1864
April
20
a 277-5°
8 34-6°
30
206
89
0-9829
0-955
• •
?
Contempor¬
ary Lyrid
orbit
1950
April
21
a 271°
8 31°
305
210
81
0-88
0-90
46-6
19-8
41
At the descending node, the comet approaches to within 0-002 a.u. of
the earth’s orbit, and the connexion of the Lyrid shower with the comet
is highly probable. The great age for which the shower has been active
is no doubt due to the high inclination (80°) of the orbit which makes
planetary perturbations improbable.
4. The 77-Aquarid shower
(a) History
The 77 -Aquarid shower occurs early in May with an hourly rate ot
about 10 in the northern hemisphere and 20-30 in the southern hemi-
t Loc. cit. on p. 262.
x Guile, J. G., loc. cit.
264 THE MAJOR METEOR SHOWERS—I XIII, §4
sphere. There are no well-attested cases of any spectacular past occur¬
rences of this shower, although Olivieri mentions that if the node were
stationary the showers of a.d. 401 April 9 (= a.d. 1850 April 29), a.d.
839 April 17 (= a.d. 1850 April 30), a.d. 927 April 17 (= a.d. 1850 April
29), and a.d. 934 April 18 (= a.d. 1850 April 30) in Newton’s listsJ
might possibly be past displays of ij-Aquarids. Nevertheless, consider-
Fio. 131. Epoch of maximum of the ij-Aquarid shower.
-x-x Observations from 1928 to 1933 by McIntosh in Now Zoaland.
-0-0 Observations in 1933 by Hoffraeister in South Africa.
able interest is attached to the shower because of its possible connexion
with Halley’s Comet. Various suggestions to this effect have appeared
since 1868,§ but it will be seen in § 4 (c) that the contemporary view on
this matter is somewhat undecided. On account of the low declination
of the radiant, the shower cannot be readily observed in the northern
hemisphere and most of the information about it comes from observa¬
tions made in South Africa and New Zealand.
(b) Activity
The activity of the 77-Aquarid stream has been established by the visual
observations of McIntosh|| in New Zealand, and of Hoffmeister|| in South
f Olivier, C. P., Meteors, ch. 8. \ Newton, H. A., loc. cit.
§ See Olivier, loc. cit., for a full account.
|| McIntosh, R. A., Mon. Not. Roy. Astr. Soc. 90 (1929), 157; 95 (1935), 601.
ft Hofhneister, C., Meteorstrdme (Weimar, 1948), ch. 8.
265
XIII, §4 PERMANENT STREAMS OF JANUARY TO JUNE
Africa. Owing to the lack of knowledge about sky conditions and
corrections for radiant altitude, no significance can be attached to
difference in hourly rates. Both series of results, winch are plottedL m
Fig 131, indicate that the maximum is attained between May 4 and May
6 that is between O = 43“ and ® = 45*. The data are summarized in
Table 88 together with the results of radio-echo observations in the
northern hemisphere since 1947, which confirm this epoch of maximum.
Table 88
Epoch of Maximum of the -q-Aquarid Shower
Date of maximum
Sun »
longitude
© {deg.)
(1928-33)
May 4-6
•.
1933
May 5
44
1947
May 4
43
1949
May 8
47
1950
May 6
45
1951
May 1$:
40
1962
May 4
43-6
Hourly raU
at maximum
10
36
7
10
12
16
15
Authority
McIntosh f
HoflineisterJ
Clegg, Hughes, and Lovoll§
Aspinall, Clogg, and Lovell||
Aspinall and Hawkinsft
Hawkins and Almond§§
Almond, Bullough, and Hawkinsllll
The shower evidently possesses a broad maximum, and the activity
extends over a considerable time. For example, in 1929 McIntosht
identified meteors from this radiant from April 21 to May 12, which
gives the breadth of the stream as about 35 x 10 6 miles. There is no
information in any of the available results which indicates any marked
annual changes in the activity of the shower.
(c) Radiant
An account of the early discussions on the radiant coordinates of the
7 j-Aquarid shower has been given by Olivier.ftt Some of the earlier
determinations were vitiated because the observers took the mean for
several successive nights, whereas OlivierJJI and Dole§§§ showed that
+ McIntosh, R. A., loc. cit. X Hoffmeister, C., loc. cit.
§ Clegg, J. A., Hughes, V. A., and Lovell. A. C. B., Mon. Not. Iioy. Aslr. Soc. 107
^ || Aspinall, A., Clegg, J. A., and Lovell, A. C. B., ibid. 109 (1949), 352.
ft Aspinall, A., and Hawkins, G. S., ibid. Ill (1951), 18.
♦ j It seonis likely that the early maximum in 1951 may be spurious, due to the masking
of the radio-echo results by a transient stream, or by a grouping of sporadic radiants.
§§ Hawkins, G. S., and Almond, M., Jodrdl Bank Annals. 1 (1952), 2.
HU Almond, M., Bullough, K., and Hawkins, G. S., ibid. 1 (1952), 22.
ttt Olivier, C. P., Meteors, ch. 8.
♦♦♦ Olivier, C. P., Publ. Astr. Soc. Pac. 22 (1910), 141.
§§§ Dole, R. M., Observatory, 44 (1921), 242.
266
THE MAJOR METEOR SHOWERS—I
XIII, §4
the radiant is a very clear case of one in daily motion. From weighted
means of the New Zealand observations referred to previously,
McIntosh! has given the ephemeris in Table 89 for the movement of the
radiant. The observations of Hoffmeister, and the radio-echo measure¬
ments referred to in ( 6 ) all give similar results for the coordinates.
Table 89
Ephemeris of the rj-Aquarid Radiant
Date
a
8
Date
a
8
1935
deg.
deg.
1935
deg.
deg.
April 28
330-4
-3-1
May 8
339-3
+ 0-2
29
331-3
-2-8
9
340-2
+ 06
30
332-2
-2-5
10
341-0
+ 10
May 1
333-1
-2-2
11
341-9
+ 1-3
2
334-0
-1-9
12
342-8
+ 1-7
3
334-8
-1-6
13
343-7
+ 21
4
335-7
-1*3
14
344-6
+ 2-5
5
336-6
-0-9
15
345-5
+ 2-9
6
7
337- 5
338- 4
-0-5
-01
16
346-4
+ 3-3
(d) Velocities
There is scarcely any published information on the velocity of meteors
of the 77 -Aquarid stream. The paucity of data is well illustrated by the
fact that in the entire published data of the British Astronomical
Association since 1890 only two doubly observed rj-Aquarid meteors
are listed.J The first was a very bright meteor observed on 1900 May 3.
The data were reduced both by Denning and by Herschel with the
following results:
Denning a 337°, 8 ±0° v = 45 km./sec.
Herschel a 335°, 8—2° v = 37 to 43 km./sec.
More recently, Porter§ has corrected the data and gives
a 327°, 8 + 6 ° v = 38 km./sec.
For the second, observed on 1921 May 4, Porter gives
a 308°, 8 +10° v = 68 km./sec.
The theoretical parabolic velocities, calculated from the elongations, are
68 and 67 km./sec. respectively.
t McIntosh R. A., loc. cit.
t Mem. Brit. Aslr. Am. 10 (pt. i) (1901); Porter, J. G., Mon. Not. Boy. Aslr. Soc.
103 (1943), 134.
§ Porter, J. G., loc. cit.
268 THE MAJOR METEOR SHOWERS—I XIII, §4
Recently a certain amount of information on the rj -Aquarid velocities
has been obtained from the radio-echo measurements. In 1951 Hawkins
and Miss Almondf measured three ij-Aquarid velocities as 63-7,63-0, and
58-8 km./sec. Also, in the velocity measurements made by McKinley J and
discussed in Chapter XII, a peak in the distribution between 1949 May 3
and 6 (Fig. 114) can be identified with the 77 -Aquarid shower, and
indicates a mean velocity of 64 km./sec.
Fio. 132. Tho orbit of the ij*Aquarid meteor stream, as calculated by Miss
Almond from the radio-echo data, compared with the orbit of Halley's Comet.
(e) Orbit
Full details of the discussions which centred around the orbit of the
rj -Aquarid stream and its relation to Halley’s Comet have been given by
01ivier.§ Table 90 gives Olivier’s results for the orbital elements of the
stream, these being a weighted mean of the elements computed for
eight radiants derived from observations of about ninety meteors.
Tho elements are calculated in two ways: firstly by assuming a parabolio
velocity for the meteors, and secondly by assuming that they have the
f Hawkins, G. S., and Almond, M., Jodrcll Bank Annals, 1 (1952), 22.
♦ McKinley, D. W. R.. Astrophys. J. 113 (1951), 225.
§ Olivier, C. P., Meteors, ch. 8.
XIII, §4 PERMANENT STREAMS OF JANUARY TO JUNE
same major axis as Halley’s Comet. Also given in Table 90 are the
orbital elements calculated by Hoffmeisterf for the meteor stream, and
those calculated by McIntosh}; from the New Zealand observations.
Olivier, Hoffmeister, and McIntosh considered that the elements of
the orbit as given in Table 90 were in good enough agreement to justify
the belief that the meteor stream is associated with Halley’s Comet,
and it was beUeved that the Orionids (see Chapter XV) were also
associated with this comet. Recently, however, Miss Almondf has
computed the orbit of the stream on the basis of the velocity indicated
by the radio-echo measurements referred to above, 64 km./sec. Taking
the radiant as a 338°, 8 ±0° on May 4, the orbital elements are given in
Table 90, and the orbits are plotted in Fig. 132. The period of the shower
appears to bo 11 years, that is only about one-seventh of that of Halley’s
Comet. The orbit is, however, closely aligned with that of the comet
after perihelion. At the ascending node the calculated orbit again passes
close to the orbit of the earth on November 21, that is a month later than
the date of the Orionid shower. Further velocity determinations of
greater accuracy are evidently necessary before this interesting situation
can be fully clarified.
f Hoffmoiator, C., Astr. Nachr.
J McIntosh, R. A., loc. cit.
196 (1913), 309.
§ Almond, M., Jodroll Bank, unpublished.
XIV
THE MAJOR METEOR SHOWERS—II
THE PERMANENT STREAMS OF JULY AND AUGUST
After the 77 -Aquarid shower in early May, the night-time activity
remains very low until late July, the major events being concentrated
in the day-time sky (Chapter XVHI). The period of late July and
August is, however, one of the richest of the whole year, and contains
two major showers (the 8 -Aquarids and the Pereeids) and a large number
of streams of a min or character, some of which—such as the a-Capricor-
nids, Cygnids, and Lacertids—are the best known and the most active
of the minor streams.
1. The 8-Aquarid shower
(а) History
The 8 -Aquarids attain a maximum about July 28. The shower has a
low declination and is most readily observed in the southern hemisphere—
it is, in fact, perhaps the most prominent of the showers visible in the
southern hemisphere. In his records of ancient showers, Newtonf lists
two (a.d. 784 July 14 and a.d. 714 July 19) which correspond to the
epoch of the 8 -Aquarids (1850 July 29 and 1850 August 2 respectively)
and which Olivier J considers to be notable past occurrences of this
shower. Apart from this, there are no records of unusual occurrences of
the shower during the period of its observation by trained observers
since the second half of the nineteenth century.
(б) Activity
Plots of the hourly rate of the shower according to observations made
by Denning§ in the northern hemisphere between 1869 and 1898, and by
McIntosh|| in New Zealand between 1926 and 1933 are shown in Fig. 133.
Both sets of observations agree in showing a rather rapid rise to maxi¬
mum on July 28 followed by a slow decrease. Information on the shower
has also been given by Hoffmeister.tt who, whilst agreeing with the
general trend of the activity as shown in Fig. 133, places the maximum
at O = 130° (August 3). In the accompanying diagram,JJ however, the
t Newton, H. A., Amer. J. Set. ( II ), 36 (1863), 146; 37 (1864), 378.
I Olivier, C. P., Meteor*, ch. 6 (1925).
§ Denning, W. F., Mem. Roy. Astr. Soc. 53 (1899), 203.
|| McIntosh, R. A., Mon. Not. Roy. Astr. Soc. 94 (1934), 683.
tt Hoffmeister, C., MeleorstrGme (Wiemar, 1948), ch. 9.
XX Hoflmeistor, C., ibid., ch. 9, fig. 29.
XIV, §1 PERMANENT STREAMS OF JULY AND AUGUST
271
Fio. 133. The epoch of maximum of the SAquarid shower.
_ 0 --#—Denning 1869-98. -x-x-McIntosh 1926-33.
maximum is shown at 0 = 122° (July 26); hence it is not possible to
attach any significance to this discrepancy. Moreover, the recent radio¬
echo observations! give data in agreement with the Dcnning-Mclntosh
results as follows:
Hourly rate
Maximum
©
(see note in text)
1949 July 29
125°-8
24
1950 July 28
124°-5
38
1951 July 27
123°-4
41
As regards the hourly rate given by the radio-echo observations, owing
to the low declination of the radiant it was not possible to separate the
8-Aquarid stream from the appreciable sporadic background rate. Hence
these figures include both the sporadic and 8-Aquarid rates, and are to
be compared with the total rates given by McIntosh,J at the maximum,
of 34 per hour. Lindblad§ has published details of some radio-echo
observations of the 8-Aquarid shower made in 1950. He interprets
the results as indicating a maximum on July 28-29 in agreement with the
visual results, but he also finds evidence that a large number of very
faint 8-Aquarids crossed the earth’s orbit 3-5 days before the main
stream. Lindblad attributes this separation to the Poynting-Robertson
effect (see Chap. XX).
f Hawkins, G. S., and Almond, M., Mon. Not. Roy. Astr. Soc. 112 (1952), 219.
I McIntosh, R. A., loc. cit.
§ Lindblad, B. A., Meddl.fr. Lunds Astronom. Obs. (1950), Ser. I, no. 179 (1952).
272
THE MAJOR METEOR SHOWERS—II
XIV, § 1
(c) Radiant
The most complete radiant data are those given by Mclntoshf from the
observations made in New Zealand between 1926 and 1933 and shown
in Table 91. Also tabulated for comparison are the radiant coordinates
given by Hoffmeister.t Hoffmeister states that the radiant is very
diffuse and that the concentration does not greatly differ over 20°. The
radiant is unfavourably placed for radio-echo determinations in the
northern hemisphere, but the following information given by Hawkins
and Miss Almond§ may be compared with Table 91.
O (1950) 124°-5 a = 339°, 8 = -14°, diam. 3°.
O (1951) 123°*4 a = 336°, 8 = 0°, diam. 6°.
Table 91
Radiant Coordinates of the h-Aquarid Stream
McIntosh
Hoffmeister
Date
0 1951
a
5
“
3
July 22
118° 22'
deg.
334-9
deg.
• •
23
119 19
335 8
• •
24
120 17
336-8
1*T1
• •
25
121 14
337-7
18-1
• •
26
122 11
338 6
17-7
333 0
— 13-0
27
123 09
339 6
17-4
• •
• •
28
124 06
340-5
17-0
• •
• •
29
125 03
341-4
16-6
• •
• •
30
126 01
342-4
16-3
• •
• •
31
126 58
3433
159
• •
• •
Aug. 1
127 65
344 3
15-9
342-4
-17-7
2
128 53
345 1
15-1
• •
• •
3
129 50
346-0
14-8
• •
• •
4
130 48
3469
14 4
• •
• •
6
131 45
347-8
14-0
• •
• •
6
132 43
348-7
13-6
341-6
-17-2
7
133 40
349-7
13-1
• •
• •
8
134 38
3506
12-7
■ •
• •
9
135 35
351-5
12-2
346-5
-16-5
10
136 33
352-4
11-8
• •
• •
The various observations are in reasonable agreement, but undoubtedly
the greatest weight must be attached to the New Zealand observations
where the radiant appears near the zenith, and where, according to
| McIntosh, R. A., loc. cit.
X Hoffmeister, C., MeteorstrSme (Weimar, 1948), ch. 9.
§ Hawkins, G. S., and Almond, M., loc. cit.
273
XIV §1 PERMANENT STREAMS OF JULY AND AUGUST
McIntosh, the spread of the M
of the radiant point by about one degree in right ascension 1
^ThetTare few published velocity measurements for the ^Muand
shower. For example, all the visual data collected by PorterJ yield
only six measurements of possible S-Aquarid velocities
spread over a very wide range, as shown in Table 92.
Table 92
Visual Velocity Measurements of possible S-Aquarid Meteors
Date
a
S
Measured
velocity
Theoretical parabolic
velocity
1898 July 30
1898 Aug. 11
1899 Aug. 1
1923 Aug. 2
1924 July 24
1924 July 29
deg.
340
343
336
346
317
333
deg.
-21
-12
-16
-16
-27
-16
km. 1 tec.
55
19
32
74
14
30
km./sec.
46
43
44
49
37
44
Prentice? quotes a mean observed velocity of 29 km./sec but the sources
of the individual data are not given. The theoretical parabohe geocentric
velocity for the six possible 8-Aquarids is given in column 5 of Table 92.
The value given by Prentice? of 29 km./scc. for the geocentric velocity
corresponds to a heliocentric velocity of 32km./sec. Hoffmeister|| quotes
a heliocentric velocity of 34-6 km./sec. Mclntoshtt calculated a value
of 54-1 km./sec. (that is a hyperbolic orbit) from the zenith attraction
of the radiant. However, Davidson}* later showed that the method
used by McIntosh for calculating the velocity was incorrect.
Recently it has been possible to measure the velocity of the shower
by the radio-echo technique. Thus in the work on the sporadic distribu¬
tion McKinley?? gives a velocity distribution for the period 1949 July 26-
29 with a sharp peak centredat 40-41 km./sec. (Fig. 114, Chap. XII). Miss
Almondllll has also given the results of a specific experiment to measure
+ Whipple. F. L.. Sky and Tducopt, 6 (1947). no. 70. 10; states that unpublished
ohotoeraphic results indicate that the radiant is difluse.
t Porter, J. G., Mon. Not. Roy. Astr. Soc. 103 (1943), 134.
§ Prontico, J. P. M., Phys. Soc. Rep. Prog. Phys. II (1948), 389.
|| Hoffmeister, C., Meteorstr6me (Weimar, 1948).
+t McIntosh, R. A., Mon. Not. Astr. Soc. 96 (1936), 704.
tt Davidson, M., ibid. 97 (1937), 75.
§§ McKinley, D. W. R., Astrophys. J. 113 (1951), 258.
||l| Almond, M., Jodrell Bank Annals, 1 (1952), 22.
274 THE MAJOR METEOR SHOWERS—II XIV, § 1
the 8-Aquarid velocities using the Jodrell Bank technique. There were
155 velocities measured using a dipole aerial in the period 1952 July
26-29, but the stream was not sufficiently prominent over the sporadic
background to yield a measurable velocity group. On the other hand,
with the more directive aerials of equipment IV (Chap. XII), used
during transit of the 8-Aquarid radiant between 02h. and 03h. on 1952
July 28,29, thirty-seven velocities were measured with a prominent group
Fio. 134. The volocity distribution of 8-Aquarid motoore
as measured by the radio-echo technique.
as shown in Fig. 134. Thirty-five of the velocities were between 35 and
49 km./sec. with a mean of 40-5±2-7 km./sec. The remaining five, which
are shown shaded in Fig. 134, had large deviations from the root mean
square value and were probably sporadic. In order to show that the
grouping was characteristic of the 8-Aquarid shower, a check experiment
was made under similar conditions on 1952 August 8. No grouping of
velocities was found.
(e) Orbit
Orbital elements for the 8-Aquarid stream have been given by
McIntosh f and Watson, J assuming a parabolic velocity, and by Hoff-
meister,§ assuming his indirectly derived value for the heliocentric
velocity of 34-6 km./sec. Orbits based on the actual velocity measure¬
ments have been calculated by Lindblad,|| using McKinley’s velocity and
the McIntosh radiant, and by Miss Almond,|t using her own velocity
f McIntosh, R. A., loc cit. (1934).
x Watson, F., Between the Planets (Blakiston).
§ Hoffmeister, C. f Meteorstr6mc (Weimar, 1948).
|| Lindblad, B. A., loc. cit.
ft Almond, M., loc. cit.
XIV, §1 PERMANENT STREAMS OF JULY AND AUGUST
measurements and the McIntosh radiant. The various results are given
in Table 93.
Table 93
Orbital Elements for the 8 -Aquarid Meteor Stream
ft
n
■— j
to
i
e
q
a
Velocity
heliocentric
I.r*
deg.
deg.
deg.
deg.
a.u.
a.u.
Km. /*«c.
McIntosh
assumed
parabolio
(1034 July
28) .
304-7
104 3
55-8
10
0-0393
••
Watson
306
••
••
56
10
0 039
• •
assumed
parubolio
lloffinoistor
(Aug. 3) .
310-0
97-0
147-0
23 7
09264
0-118
1-5996
34-64
Lindblad
(July 29) .
306-6
• •
152-2
28 4
0960
0-080
1-807
354
Almond
(July 28) .
Comot 1948 n
1606 Icarus
304-6:1; 1
233-0
87-777
101 ±2
• •
166±2
183-8
30-876
24±6
1325
23-02
0 96±0 2
0-809
0-82697
0-06 ±
0-015
0-558
0-187
1-6+0 6
-03
2-922
1-0784
• •
• •
• •
The orbits given by Lindblad and Miss Almond are very similar, and
since they are based on actual velocity measurements they must be
regarded as significant. The errors given in Table 93 for Miss Almon s
orbit indicate the effects of the spread in the measured velocity. 1 he mean
orbit, projected on to the plane of the ecliptic, is shown in Fig. 135. I his
orbit is very similar to that of a prominent day -time stream—the Anctids
-and the relationship between the two will be discussed in Chapter
XVIII. On account of the very elliptical nature of the orbit, there are few
bodies in the solar system with which the stream is likely to be associated.
Rigollett suggested that the shower might be associated with Comet
1948 n which has a markedly elliptical orbit, but the closest approach
is 0’22 a.u. and the association does not seem plausible. Rigollett has
also suggested that the stream may be associated with the minor planet
1566 Icarus discovered on 1949 June 26 by Baade. The orbital elements
for the comet and for Baade’s object are tabulated in Table 93 and also
shown in Fig. 135 for comparison with the 8-Aquarid orbit.
2. The Perseid shower
(a) History
The Perseid meteor shower is one of the most regular visible meteoric
events, yielding hourly rates of about 50 over the period of maximum
t Rigollet, R., Ann. d'Astrophys. 14 (1951), no. 2.
x Rigollet, R., Documentation des Obs. Inst. d'Astrophys. 6 (Paris, 1952).
276 THE MAJOR METEOR SHOWERS—II XIV, §2
Fio. 135. The orbit of the S-Aquarid stream, computed from the radio-echo
observations by Miss Almond. The orbits of comet 1948 n and of Baade’s object
1566 Icarus are shown for comparison. Projection is on the plane of the ecliptic.
from August 10-13 each year. It also extends for a considerable time
on either side of the maximum with reduced hourly rates. The history
of the shower, which can be traced back for over 1,200 years, has been
described by Olivier.f The existence of the regular display in August
t Olivier, C. P., Meteors, ch. 6.
XIV, §2 PERMANENT STREAMS OF JULY AND AUGUST
was first recognized in the period 1830-40 by Qudtelet, Herrick, and
others, since Chen the shower has been observed Bystemat.c^ The
shower is particularly noteworthy because the comput ationof t bt
by Schiaparellit between 1864 and 1866 led to the estabhshment of hc
connexion between it and Comet 1862 III, this being the first occasion
on which any plausible relation was established between meteors an
(6) Activity
One of the most complete investigations of the Perseid shower was
made by Denning* during the years 1869-98. Between the dates of
July 11 and August 19 he observed 6,479 meteors, 2,409 of which he
identified as members of the Perseid stream, with hourly rates as shown
in Fig. 136. The motion of the radiant point during this period will be
referred to in (c). Subsequent observations have confirmed the general
shape of the epoch of maximum as given by Denning. For example,
Fig. 136 also gives the results of Opik’s§ observations made in Esthonia in
t Schiaparelli, G. V., SUmschnuppen.
$ Denning, W. F., Astr. Nachr., no. 3546.
§ Opik, E. J., Publ. Tartu Obs . 25 (1922), no. 1.
278 THE MAJOR METEOR SHOWERS—II XIV, § 2
1920, of the radio-echo observations! made in 1950, and of contemporary
visual observations-! (The change of the epoch of maximum with date
is apparent only. All maxima coincide when the scale is reduced to solar
longitude.) The identity of the stream before July 28 and after August
17 is uncertain. Bredikhine§ first questioned the reality of these Perseid
radiants derived from such low hourly rates at a time of the year when
the activity is so complex. Since the visible sporadic rate in late July
is about 20 per hour, it is evident that the observations of the Perseid
stream when the hourly rate is less than about three or four cannot have
great significance.
Even though the Perseid display is regarded as being constant in
hourly rate, there have nevertheless been some significant changes.
The ‘normal rate’ for a single observer under good sky conditions is
generally given as about 50 per hour; but there have been several notable
occurrences, the last of which, in 1921, gave an hourly rate of 250. On
other occasions the returns have been very poor, particularly in 1911
and 1912, when, with only a few per hour, Denning|| suggested that the
shower might have disappeared.
Table 94 gives the hourly rate of the shower since 1900 as far as the data
can be extracted from the very dispersed references. Where bad sky
conditions or moonlight interfered with the observations, the observers
estimate of the hourly rate has been quoted. Except where otherwise
indicated, the results are those obtained by the observers of the British
Astronomical Association.!! Various predictions have been made regard¬
ing a periodicity in the shower. For example, Denningtabulated all
the accounts of the ancient and modem displays of the Perseids going
back to a.d. 714 July and decided that a period of 11-72 years was sug¬
gested by these observations. He predicted future maxima in 1932-88,
1944-60, 1956-32, 1968-04, but there is no evidence for any unusual
return of the shower on the first two of these dates.
(c) Radiant
Early studies of the radiant position of the Perseids are unique in that
they first demonstrated clearly the daily motion of a radiant point.
t Hawkins, G. S., and Almond, M., Mon. Not. Roy. Astr. Soc. 112 (1952), 219.
x Hawkins, G. S., measurements for 1944-7.
§ Bredikhine, T., Bull. Imp. Nat. Moscow, 1 (1888).
|| Denning, W. F., Observatory, 35 (1912), 337.
ft Abstracted from the Memoirs and Journals of the British Astronomical Asso¬
ciation.
XX Denning, W. F., Mon. Not. Roy. Astr. Soc. 84 (1923), 45; 84 (1924), 178.
XIV, §2
PERMANENT STREAMS OF
JULY AND AUGUST
279
Table 94
Hourly Rale of the Perseid Stream since 1900
Year
1901
Aug. 10
55
Aug. 11
49
Aug. 12
• •
Aug. 13
• •
60
1902
1903
15
• •
• •
• •
30
• •
a a
1904
92
37
• •
• •
• •
1906
10
• •
a
• •
1907
71
30
• •
e •
1908
15
• •
• •
1909
12
67
• •
• •
• •
1910
46
• •
• •
1911
2
1
• •
1912
2
12
• •
4)0
1916
1920
1921
(78)
(33)
(196)
(250) 250
(77)
(93)
(44) Opikt
(43) Opikt
1924
weak
• •
• •
• •
1925
weak
• •
• •
• •
• ®
1926
avorage
• •
• •
1927
weak
• •
• •
• •
1928
• •
33
• •
• •
1929
weak
• •
• •
• •
1930
1931
1932
weak
• •
24
• •
73
48
64 (160)
• •
• •
Olivior gives 160
PrenticoJ
1933
1934
woak
18
29
• •
• •
• •
PronticeJ
1935
19
• •
• •
»*
1936
• •
• •
12
1939
13
35
25
•*
1940
1946
1947
18
(18)
29
(23)
23
(46) 26
•*
Radio-echo data§
(27)
1948
^ —
• •
• •
(21) 57
(10) t» **
1949
1950
(14) 24
21
57
64
*» *•
(16)59 „
1951
31
37
(44) 32
33 »• »t
1952
22
39
50
36 m »*
1953
22
26
37
22 „ »•
t The values in parentheses for 1920 and 1921 ore those given by Opik E.
Tartu Obs. 25 (1922-4), nos. 1 and 4), obtained by his statistical doub , are
Se rates are therefore not strictly comparable with those given «>'^ero w »ueh «o
the unreduced rates for a single observer. Even so. there is.no douM from the records
of many other observers that the shower of 1921 was exceptionally strong.
X From observations of the British Astronomical Association privately commum
COt § e The values*^ pwcnthcscs aro from the visual records of the B.A.A. (sco }).
280 THE MAJOR METEOR SHOWERS—II XIV, §2
%
Olivierf assigns the credit for this discovery to Twining}; although
Denning’s§ great series of observations showed that the motion existed
over a considerable period of time, placing the matter beyond dispute.
Discussions of the motion of the Perseid radiant have been given by
Denning§ and by King.|| Table 95 compares the average positions given
Table 95
Radiant Positions of the Perseid Shower
Visual
Radio echo
King
Opik
1950
1951
1962
Date
a 8
■
8
tt
8
a
8
a
8
a
8
July 27
deg. deg.
deg.
deg.
deg.
deg.
deg.
deg.
deg.
deg.
deg.
deg.
25 +62
27-1 + 53-2
28
28 63
28-2
636
•
•
0
29
• •
29 3
53-8
.
28 +62
•
30
• •
30-6
64-1
.
31
66
•
31
• •
31 6
64 4
•
40
68
Aug. 1
• •
32-7
64-7
.
38
56
2
• •
33 9
65-0
.
42
65
3
34 8 66
35-1
55 3
.
.
.
40 +60 |
41
+ 67
4
36 67
36-4
55-5
•
9
42
63
39
61
5
• •
376
65-7
•
•
•
• •
6
38 56 5
389
560
.
33
62
39
39
66
7
• •
40-2
66-2
38
+ 66
69
45
83
41
68
8
• •
41-6
666
•
42
67
43
67
39
62
9
42 67
429
66-7
41
56
43
66
43
67
42
57
10
44 67-2
443
66-9
40
66
44
57
47
59
44
65
11
454 57-4
457
67-1
36-42
56-58
45
61
49
46
44
68
12
47 1 57-5
47-1
67-3
38
66
46
67
46
57
48
61
13
47-7 68 3
48-5
67-5
40
67
61
69
44
60
49
69
14
48 9 68-3
600
67-7
..
52
61
48
58
64
69
15
605 685
51-4
67-8
..
61
62
37
68
• •
16
• •
62-9
680
• ■
49
66
65
69
• •
17
• •
64 4
68-2
• ■
47
62
43
60
• •
by Denning and King, from which it will be seen that the general position
and motion are well established. As a result of the observations in 1921,
Opiktf referred to the fact that the radiant covered a considerable area
and gave the mean radiants as listed in Table 95. According to Prentice,};}:
contemporary visual observations show that the Perseid radiant is very
diffuse, with a diameter of 10-15°, the centre of which moves roughly as
t Olivior, C. P. t Meteors, ch. 5.
X Twining, A. C., Amer. J. Set. (II), 32 (1861), 444.
§ Donning, W. F., Mem. Roy. Astr. Soc. 53 (1809), 203; Mon. Not. Roy. Astr. Soc. 62
(1901), 161.
|| King, A., Mon. Not. Roy. Astr. Soc. 76 (1916), 542; 88 (1927), 113.
tt Opik, E. J., Puhl. Tartu. Obs. 25 (1923), no. 4.
XX Prentice, J. P. M., private co mm u n ication.
281
XIV, 52 PERMANENT STREAMS OF JULY AND AUGUST
indicated in Table 95. The radio-echo observation^ of the
position, also given in Table 95 for 1950, 1951, and 1952, “
siderable scatter about these mean positions. This is to. ® iUon is
a diffuse radiant with active subcentres, smce the radian p
determined for only a short period during the passage of radian^
through the beam. The mean radiant assigned by Prent J
Fio. 137. Tho paths of ton Pereoid trails photo¬
graphically recorded near the time of maximum
between© = 139 # 02 and 139°-76.
period of the maximum is a 44°, 8 +58° and it is classed as 'diffuse'. On
the other hand, in a preliminary account of the photographic work on
the Perseid meteors, Whipplc§ states that at the time of maximum tue
radiation is from a relatively small area of the sky. This is well illustrated
in Fig. 137, which shows the paths of ten trails photographically recorded
between solar longitude 139°*02 and 139°*76.
The data for nine doubly photographed Perseid meteors have been
given by Whipple,§ and the results are plotted in Fig. 138. The radiant
motion is clearly in evidence. Whipple’s values for the daily motion are
Ac = -f 0°-7 per day, A8 = + 0°1 per day. The inclusion of forty-nine
singly photographed Perseid trails indicates the possibility of there
being two moving Perseid radiants, the major one after August 7 and a
minor one before August 9, but more observations are needed to verify
this duplicity. The daily motion of the radiant from the smoothed radio¬
echo data is Ac = +0°-6, A8 = +0°-l, in agreement with Whipple's
value but differing from the values of Ao = +l°-3, A8 = +0°-3 given
by Denning.
t Hawkins, G. S., and Almond, M., Mon. Not. Roy. Aetr. Soo. 112 (1952), 219 (except
data for 1962 which aro unpublished).
t B. A. A. Handbooks.
§ Whipple, F. L., Sky and Telescope, 6 (1947), no. 10, 10.
282
THE MAJOR METEOR SHOWERS—II
XIV, §2
Fio. 138. The radiant positions of nine doubly photographed Persoid
meteors, showing the daily motion of the mean radiant (full line).
Each radiant is plotted in its actual position and joined by a broken
line to the point on the mean path which corresponds to the time of
observation of the meteor. The sun's longitude is given for each
observation (© «■ 139° s Aug. 12). R 9 is the mean radiant position.
(d) Velocities
The analysis of the visual meteor data collected by Porterf gives 47
cases of possible Perseid velocities as listed in Table 96. There are 20
determinations from multiple observations and 27 from duplicate
observations.
The mean velocity from the multiple observations is 62 km./sec. and
from the duplicate observations 65 km./sec. In his analysis of the data
Porter J later gives a mean value of 43-4 km./sec. for 152 Perseids occur¬
ring within the time limits of July 22 and August 19; but the individual
details of the reductions additional to the forty-seven listed in Table 96
are not given. This figure of 43-4 km./sec. for the Perseid velocity is also
quoted by Prentice§ as the result of the British visual measurements.
The velocities of two Perseid meteors were measured in the photo¬
graphic work of Millman and Miss Hoffleit|| using the rotating-shutter
technique described in Chapter XI. The velocities were 50 and 41
km./sec.; they regarded the low values as due to retardation in the
earth*8 atmosphere.
The velocities of several Perseid meteors have been accurately deter¬
mined by Whipple and by Jacchia using the double-camera technique.
t Porter, J. G., Mon. Not. Roy. Astr. Soc. 103 (1943), 134.
x Porter, J. G., ibid. 104 (1943), 20.
§ Prentice, J. P. M. t Rep. Phys. Soc. Prog. Phys. 11 (1948), 389.
|! Millman, P. M., and Hoffleit, D., Ann. Harv. Coll. Obs. 105 (1937), 601.
XIV, §2 PERMANENT
STREAMS OF JULY AND AUGUST
283
Table 96
Visual Velocity Measurements of Possible Perseid Meteors
I. From multiple observations
Date
Radiant
a 8
deg. deg.
Measured
velocity
km./sec.
Theoretical parabolic
velocity
km./sec.
1899 Aug.
9
10
41
43
+ 58
63
71
36
61
64
10
44
58
104
61
10
42
56
68
62
r a
1924 Aug.
2
6
63
37
58
65
40
29
69
62
a r
1932 Aug.
11
11
63
40
50
59
34
45
65
61
11
65
68
39
60
11
46
57
49
62
11
48
44
40
68
11
66
47
45
65
11
49
54
52
63
11
50
52
42
64
11
34
60
37
60
11
38
55
116
62
11
62
56
63
62
1939 Aug.
11
58
58
48
60
11
45
65
41
62
1940 Aug.
10
38
38
45
69
Mean of multiplos ■■
62 km./ boo.
II. From duplicate observations
1877 Aug. 7
55
55
80
62
10
43
52
47
64
10
56
65
220
57
1895 Aug. 11
49 60
61
60
11
37
57
56
61
11
33
52
29
63
1897 Aug. 8
52
46
50
66
9
49
55
146
62
1898 Aug. 10
54
23
120
72
10
48
52
45
64
11
47
55
60
63
11
53
56
61
62
11
48
68
63
61
1899 Aug. 6
41
57
60
61
11
45
58
81
61
11
45
57
69
62
14
53
47
36
67
1901 Aug. 15
53
53
62
64
1902 Aug. 12
61
56
61
62
1922 July 28
36
43
45
66
30
38
45
60
66
Aug. 15
60
74
18
52
1923 Aug. 10
42
58
55
61
11
48
53
48
64
12
42
58
42
61
13
50
58
63
61
1924 July 31
38
49
28
64
Mean of duplicates =
65 km./sec.
284
THE MAJOR METEOR SHOWERS—II
XIV, §2
Complete details for one (No. 689) have been given by Whipplef and
the velocities, decelerations, and heights for nine others by Jacchia.J
These are listed in Table 97.
Table 97
Perseid Velocities Photographically determined by the Double-camera
Method
Harvard serial
number
Date
Velocity
689
1937 Aug. 15-2565
km./sec.
61-188
978
1940
99
8-19
69-95
1089
1941
99
11-30
69-88
1173
1942
99
6-18
69-76
1377
1943
99
7-27
60-88
1273
1945
99
11-34
69-23
1273
1945
99
11-34
68-83
1275
1945
99
12-32
60-04
1276
1945
99
12-35
68-54
1469
1947
99
13-24
mam
The close agreement of these ten velocities, with a mean value of
59-85 km./sec., is in striking contrast to the wide scatter of those deter¬
mined by visual observations (Table 96).
Ceplecha§ has given details of a Perseid photographed at three stations
in Czechoslovakia, the velocity being 59-646 km./sec., in excellent agree¬
ment with the results of Table 97.
Radio-echo measurements of the velocities have recently been made
in America, Canada, and Great Britain. One accurately determined
velocity using a three-station ‘moving-head’ Doppler technique (see
Chap. IV) has been discussed by McKinley.|| This Perseid was recorded
on 1949 August 11. The mean value from the moving-head records was
59-8 km./sec. and from the Doppler records 58-3 km./sec. The velocities
at the beginning and end of the recorded path were 61-0 and 58-5 km./sec.
respectively. These results are in excellent agreement with the photo¬
graphic determinations listed in Table 97.
Manning, Villard, and Petersonft used the Doppler technique at Stan¬
ford during the night of 1948 August 11-12 and measured sixty velocities,
t Whipple, F. L., Proc. Amer. Phil. Soc. 79 (1938), 499.
x Jacchia, L. G., Tech. Rep. Harv. Coll. Obs. (1948), no. 2 (Harvard Reprint Series
11-26).
§ Coplecha, Z., Bull. Cent. Astr. Inst. Czech. 2 (1951), no. 8, 114.
|| McKinley, D. W. R., J. Appl. Phys. 22 (1951), 202.
tt Manning, L. A., Villard, 0. G., and Peterson, A. M., J. Appl. Phys. 20 (1949), 476.
(Stanford Technical Rep., Sept. 30, 1948, no. 7).
285
XIV, §2 PERMANENT STREAMS OF JULY AND AUGUST
from which it was possible to isolate six Perseids, the average velocity of
which was 62-3±l-6 km./sec.
Table 98
Radio-echo Measurements of Perseid Velocities
Date
No. of
determinations
Mean velocity
km./sec.
Remarks
f 59*8
McKinley,f moving-head echo
1949 Aug. 11
1
\58-3
Doppler whistle
1948 Aug. 11-12
6
62-3± 1-6
Manning, Villard, and Peterson*
1948
27
60-7±4-7]
1949
14
60-3±2-9
Hawkins and Miss Almond§
1950
41
610±60
1951
83
69-2±5-3
The radio-echo measurements made at Jodrell Bank during the
showers of 1948-51, inclusive, using the pulsed diffraction technique,
have been summarized by Hawkins and Miss Almond.§ The details are
included in Table 98, together with the other radio-echo measurements,
and the distribution of velocities is shown in Fig. 139.
Hawkins and Miss Almond have investigated how much of the disper¬
sion in the velocities might be caused by an actual spread of the velocities
in the stream. The details of the analysis have been described on p. 255
t McKinley, D. W. R., J. Appl. Phys. 22 (1951), 202.
t Manning, L. A., Villard, O. G. and Poterson, A. M., ibid. 20 (1949), 475.
§ Hawkins, G. S., and Almond, M., Mon. Not. Roy. Astr. Soc. 112 (19o2), 219.
286 THE MAJOR METEOR SHOWERS—II XIV, § 2
in connexion with the Quadrantid velocities. Using the same notation,
the corresponding values for the Perseids over the years 1948-51,
inclusive, are o E = 1-7 km./sec.; o s = 2-9 km./sec.; a R = 2-1 km./sec.;
a A = 0-3 km./sec., and, since o 0 = 4-6km./sec., c H = 2-3 km./sec. Thus
the actual spread in heliocentric velocities may make a significant con¬
tribution to the dispersion of the velocities in Fig. 139.
Fio. 140. The orbit* of the Pereeid meteor stream as determined by the radio-
echo observations compared with the orbit of Comet 1862 III. (Projection is
on the plane of the comot's orbit.)
(e) Orbit
As mentioned in (a) above, the work of Schiaparelli on the orbit of the
Perseids provided the first clear illustration of the connexion between a
meteor stream and a comet. The final calculation of the parabolic orbit
for the Perseids was made by Schiaparelli,t based on A. S. Herschel’s
determination of the radiant in 1863 as a = 44°, 8 = -+-56°. The elements
are given in Table 99 compared with Comet 1862 III.
More recent computations of the orbit using the photographic and
radio-echo measurements of the velocities have been given by Whipple,J
Ceplecha,§ and Hawkins and Miss Almond.|| These orbital elements are
also given in Table 99.
f Schiaparelli, G. V., Slemschnuppen ; see Olivier, loc. cit. p. 68.
x Whipple, F. L. (1938), loc. cit.
§ Ceplecha, Z., loc. cit.
|| Hawkins, G. S-, and Almond, M., loc. cit.
XIV, §2 PERMANENT
STREAMS OF JULY AND AUGUST
287
Table 99
The Orbital Elements of the Perseid Stream and of Comet 1862 III
SI
to
i
e
q
a
Period
Comot 1862 III
Schiaparelli
Whipple .
Ceplecha .
Hawkins and Almond
137° 27'
138° 16'
141° 28'
140° 21'
139° 30'
152° 46'
154° 28'
165° 31'
150° 63'
153°
113° 34'
115° 67'
119° 42'
112° 12'
114°
• •
assumed
parabolic
0-9577
0-9474
0-93
a.u.
0-9626
0-9643
0-9680
0-9506
0-97
a.u.
• •
• •
22-89
18-11
14-4
years
121-5
• •
109-5
• •
• •
The agreement of these various detcrminat.ons » very satisfactory
and the close connexion of the Perseid orbit with that of Comet 1862 III
is also evident in Fig. 140, where the orbit determined by Hawkins and
Miss Almond from the radio-echo data is projected on to the plane oi
the Comet’s orbit.
XV
THE MAJOR METEOR SHOWERS—III
THE PERMANENT STREAMS OF SEPTEMBER TO
DECEMBER
The period of September to December has long been recognized as a time
of considerable meteoric activity. In the past it has contained some
spectacular events, such as the great showers of Leonids, Bielids, and
Giacobinids. These are discussed in Chapters XVI and XVII. The
present chapter deals with the more permanent streams of the Orionids,
Taurids, Geminids, and Ursids.
1. The Orionid shower
(а) History
The Orionid shower is active from about October 15-25, reaching a
maximum on October 20-21. The hourly rate for a single visual observer
is 10 to 20, but there are no records of any outstanding displays of this
shower in the past. The shower has been the centre of great controversy,
however, firstly because it was regarded by Denning as being a clear case
of a ‘stationary radiant*, and secondly because of the probable connexion
of the stream with the rj-Aquarids and Halley’s Comet.
(б) Activity
An extensive study of the shower between 1928 and 1939 has been
made by Prentice.t The activity from 1928 to 1935 was very low, but
it increased rapidly between 1933 and 1935. Representative curves
given by Prentice t for a year of low activity (1928) and a year of high
activity (1938) are shown in Fig. 141. Prentice also investigated the
activity of the various subcentres into which the stream is divided, from
which he concluded that the activity of the sub-groups is not synchro¬
nized. The effect is shown in Fig. 142, in which the hourly rates of the
Orionids are plotted as ordinates against the years of observation for
each integral value of sun’s longitude, ©» between 205° and 210°. For
the early longitudes a decline in the hourly rate begins after 1936, but
the activity at later longitudes is still increasing. Prentice further con¬
cludes that the Orionids may have a period of about seventeen years,
t Prentice. J. P. M., J. Brit. Astr. Assoc. 43 (1933). 370; 46 (1930). 329; 49 (1939),
148; 51 (1941). 107.
X Prentice, J. P. M. (1941), loc. cit.
2PY
IS
10
I
7 938
5 r
1928 'v.
20S°
211 °
-O-J
2/3°
207° W
Longitude of Sun
Fio. Ml. Hourly rates of the Oriomds according to Prentice for years of low
(1028) and high (1938) activity.
Fio. 142. The activity of the Orionid subcentres 1928-39. (The zeros of the
ordinates are arbitrarily displaced.)
• - Observed rates, o - interpolated rates.
3595.66
U
290
THE MAJOR METEOR SHOWERS—III XV, §1
quoting observations made by Dole in America of a rich return in 1922
but one of low activity in 1925.
No subsequent observations of sufficient detail have yet been made to
enable further judgement to be taken on Prentice’s suggestion. Radio-
echo observationsf since 1946 give a fairly constant intensity for the
stream as shown in Table 100, but the resolution is insufficient to yield
any information about the activity of subcentres.
Table 100 .
Radio-echo Observations of the Orionid Activity
(c) Radiant
Denning J held strongly to the opinion that the radiant of the Orionids
was of a different character from that of the Perseids, in that it retained
a fixed place amongst the stars during the three weeks of its activity. His
observations, together with those of other British observers, showed
that there were two active radiants at a = 91°, 8 = -f 15°, and a = 97°
8 = 4-16° which remained fixed. This view of the Orionid radiant
remained almost unchallenged until 1911. Subsequent work, however,
gradually led to the abandonment of the view of such stationary radiants.
A very full discussion of the arguments surrounding these ideas has
been given by Olivier,§ and since the subject of ‘stationary radiation’ is
now closed no point would be served in discussing the matter here. In
the particular case of the Orionids, evidence was steadily accumulated
by 01ivier|| in America that the Orionid radiant was, in fact, moving in
the direction of increasing right ascension, and, during the rich shower of
1922, Doleft secured good radiants from October 17 to 29, showing the
radiant to be in motion. Also, on 1922 October 20, KingJI secured
t Hawkins, G. S., and Almond, M., Mon. Not. Roy. Aetr. Soc. 112 (1952), 219 (data
for 1961, 1952 unpublished).
t Denning, W. F., Mem. Roy. Aetr. Soc. 53 (1899), 203; JVfon. Not. Roy. Aetr. Soc.
73 (1913), 667. § Olivier, C. P., Meteore, chs. 10,11.
|| Olivier, C. P., Trane. Amer. Phil. Soc. 22 (pt. i) (1911); Mon. Not. Roy. Aetr. Soc.
74 (1913), 37.
ft Dole, R. M., Pop. Aetron. 31 (1923), 37; Publ. Leander McCormick Obe. 5 (1929), 38.
XX Bull. Harv. Coll. Obe. (1922), no. 778; (1923), no. 783.
291
XV. § 1 PERMANENT STREAMS OF SEPT. TO DEC.
photographic records of
of the expected amount from October a ^
to H. found the todtad. U.tod in T.bto .01.«-»
showing the movement of the radiant.
Table 101
Orionid Radiants 1928 according to McIntosh t
DaU
Radiant
No. of meteor a
1928 Oct. 15-66
a
deg.
89-2
5
deg.
+ 14-2
15
16-64
90-0
150
9
18-65
91-6
14-6
4
20-62
92-6
14-2
12
23-64
93-5
149
3
24-64
99-4
13-7
9
The most detailed investigation of the radiant structure has been
carried out by Prentice* between 1928 and 1939. His results not only
show conclusively that the radiant is in daily motion, but also provide a
plausible explanation of the reason why Denning was led to beheve that
the radiant was stationary. Prentice concluded that the Onomd meteors
came principally from three sharply defined centres, situated at close
intervals in declination +15°. and that these centres were in motion
parallel to the ecliptic at a rate of approximately 1-3° per day. He also
concluded that another stream was in similar motion at declination + 18.
These results are summarized in Table 102, and Figs. 143 and 144.
Table 102
Prentice's Radiants for the Orionid Stream
Loading stroam (O,)
Mid-stream (O x ) .
Following stream (0 F )
Northern stream .
Mean position at
long, of apex = 118 °
Daily motion
in a
No. of
radiants
a
8
deg.
deg.
deg.
98-1
+ 14-9
1-30
10
94-4
15-5
1-34
9
91-7
151
1-22
13
97-8
18-2
0-92
6
No. oj
meteors
46
41
60
28
t McIntosh, R. A., Mon. Not. Roy. Aatr. Soc. 90 (1929), 160.
% Prentice, J. P. M., loc. cit.
292 THE MAJOR METEOR SHOWERS—III XV, §1
The subcentres are clearly shown in the gnomonic maps of Fig. 143
which give the radiants observed on various nights in 1933 and 1935.
Finally, in Fig. 144, the right ascension of the three main streams at
1935 October 20(0 = 206 * 9 ) 1935 October 22 (o » 206 * 9 )
1935 October 23(0 = 209* 6 ) 1935 October 25(0 = 211* 6)
Fio. 143. Orionid radiants as observed by Prentice on successive days in 1933
and 1935. The notation corresponds to that of Table 102. (The P and F, streams
are additional weak centres.)
$ -f-15° are plotted against the longitude of the sun. From these
results it is clear how Denning may have been misled in his belief of
stationary radiation. Fig. 144 shows that there is considerable activity
293
XV. , , PERMANENT STREAMS OF SEPT. TO DEC.
i 2 ' i fnr several days, but that this
subcentres through *»•
not. as Denning beheved, to the existence of a stat.onary radrant m that
position.
Fio. 144. The right ascension of the three main OrionicTat| decline-
tion +15°; plotted against sun’s longitude, according to Prentice.
o - - - Observations of 1928-32. •-Observations of 1933-5.
(The six positions marked + are from duplicate accordances The others are
determinations by a singlo observer (Prentice).)
Hoffmeisterf gives details of the Orionid radiant from his own observa
tions as listed in Table 103.
Table 103
Hoffmeister's Radiants for the Orionid Stream
Year
Sun's longitude at maximum Q
Radiant
a 8
deg.
deg.
deg.
1931
203-7
95-5
+ 17-0
1933
205-6
91-0
+ 16-5
1931
205-7
92-7
+ 15-7
1933
206-1
91-0
+ 15-0
1931
207-7
97-3
+ 16-2
1933
209-9
94-5
+ 16-4
f Hoffmoister, C., Meteorstrdme, ch. 8.
294
THE MAJOR METEOR SHOWERS—III
XV, §1
From these data Hoffmeister deduces a mean value of
Omax = 206-4°, a = 93-7°±10, 8 = + 16-l°±0-3,
or, when corrected for zenithal attraction, <* 93-5°, 8 16-9°, a position
which is in good agreement with the mid-stream value given by Prentice
(Table 102).
Contemporary radio-echo observations do not compete in resolution
with the work of Prentice, but are in general agreement. The information
given by Hawkins and Miss Almondf for the years 1949-50 is as follows:
a 8 G mil
1949 95° +13° 209-5°
1950 98° +9° 207-2°
(d) Velocities
The analysis of the British visual meteor data by PorterJ contains ten
cases of possible Orionid velocities, the details of which are given in
Table 104.
Table 104
Visual Velocity Measurements of possible Orionid Meteors
Date
Radiant
Measured
velocity
Theoretical parabolic
velocity
a (deg.)
8 (deg.)
km./sec.
km./sec.
I. From multiple observations
1930 Oct. 21
95
+ 5
69
66
Oct. 25
109
+ 22
46
71
II. From duplicate observations
1928 Oct. 18
88
+ 13
65
68
Oct. 20
93
+ 15
34
67
Oct. 20
93
+ 18
33
68
Oct. 20
101
+ 16
32
70
Oct. 20
110
+ 13
21
72
Oct. 20
98
+ 19
41
Oct. 20
105
+ 25
17
71
Oct. 20
96
+ 14
68
Mean velo¬
city = 42-6
km./sec.
68
In his later analysis Porter§ gives the mean velocity of thirty-five
Orionids as 5 1 -6 km./sec., but no details are given of the other twenty-five
velocities omitted in the previous work. J The velocities of two Orionid
meteors were measured in the photographic work of Mill man and Miss
f Hawkins, G. S., and Almond, M., loc. cit.
X Porter, J. G., Mon. Not. Roy. Astr. Soc. 103 (1943), 134.
§ Porter, J. G., ibid. 104 (1944), 257.
295
XV s , PERMANENT STREAMS OF SEPT. TO DEC.
a— - -
double camera work have so far been published! as follows.
Harvard serial no.
889
1382
Date
1939 Oct. 24-40
1946 Oct. 23-29
Velocity
66-58 km./sec.
65-28 km./sec.
So far there are no records of determinations of Orionid velocities by
using radio techniques.
"KM 01ivier§ first drew attention to the simUantybetweenthe
orbits of the Orionids and of the Aquand stream of May (see Chap^
XIII) The possible connexion of the r Aquand stream w.th Halley s
Comet has already been discussed. The idea has therefore emerged that
the ri-Aquarid and Orionid meteor streams are caused by the passage o
the earth through the debris in the orbit of Halley's Comet before and
Th. *»»« for tho orbits of th<*”»
Orionids and for HaUey’s Comet are compared in Table lOo.
Table 105
Comparison of the Orbits of the V -Aquarids, Orionids, and HaUey's
Comet
Source
ft
*0
it
o
i
a
q
Orionids .
ij-Aquarids
Halloy's Comot
Mclntoshll
Jacchia 19391
Jacchia 1946 J
Sea Ch. XIII
See Ch. XIII
deg.
266
30-22
29 31
43 1
67-3
deg.
77-7
85-7
87-8
830
111-7
deg.
1033
126-1
169 0
1
0944
0-915
091
0-9673
deg.
162- 3
163- 4
162-9
160
162-2
a.u.
CO
9-84
6-32
5-0
17-946
a.u.
0-604
0-548
0-637
0-47
0 687
The connexion of the two meteor streams with the cometary orbit has
been strongly emphasized by Olivier,ft Svoboda.JJ and Hoffmc 1S ter.§§
t Millman, P. M., and Hoffleit, D., Ann. Harv. Coll. Obs. 105 (1937), 801.
X Jacchia, L. G., Tech. Rep. Harv. Coll. Obs. (1948). no. 2 (Harvard Reprint Senas
S Olivier, C. P., Trans. Amer. Phil. Soc. 22 (1911) (pt. i).
II McIntosh. R. A.. Mon. Not. Roy. Astr. Soc. 90 (1929), 160.
tt Olivier, C. P.. Meteors, ch. 8 (1925); Comets (1930). ...
XX Svoboda, J ., Bull, intemat. de VAcad.d.Sci. de Boheme, 23 (1914), 3; Astr. bachr.
§§ Hoffmeister, C., Meteorstrome, ch. 8; Die Meleore (Leipzig, 1937).
296 THE MAJOR METEOR SHOWERS—III XV, § 1
On the other hand, Porterf considers that the great distance between the
earth and the cometary orbit (0-15 a.u. at closest approach) makes any
such connexion impossible, and points out that there are thirty-five
comets which approach to within 0-05 a.u. of the earth and sixty to
within 0-1 a.u., none of which show any accordance with meteor
Fio. 146. The orbit* of the q-Aquarid meteor stream and of Halley's Comet
as given in Fig. 132, compared with two Orionid orbit* as computed by Jacchia
from photographic data.
showers. The orbit of the 77 -Aquarid stream has been compared in Fig.
132 with that of Halley's Comet. In Fig. 145 these are reproduced with
the addition of the two Orionid orbits computed by Jacchia. It is evident
that the association of the Orionids with the comet is plausible. As in the
case of the 77 -Aquarid orbit, the period is less than that of the comet.
More precise data on the orbit of the meteors are required before the
situation can be clarified.
2. The Taurid shower and the radiants in Aries
(a) History
From about October 26 to November 22, meteors can be seen from a
radiant in Taurus. The maximum, which occurs between November
t Porter, J. G., Rep. Phya. Soc. Progr. Phya. 11 (1948), 402.
297
XV. 5 2 PERMANENT STREAMS OF SEPT. TO DEC.
3 and 10 , is broad, and the
visua. observer. Nevertbe.ess, the stream ^j^ nce of
of great importance in meteor astron y • da[ly ^ otion 0 f the
the shower (nearly a month), coupled shower orbits
r adiant, led Knopff and Hoffmeisterf to conclude
were hyperbolic, and hence that the Taund -e - — on the
stream. But the investigations of Whipple* m
the radio-echo observations have shown that tins nign
Taurid shower is the return of the day-time 0-Taurid show ( P-
X VIII1 As remarked by Whipple,§ the dilution of the Taund stream
S^dt chapter as one ofthe more important known showers and
1 total population of the associated streams .s probably comparable
with that of any of the generally recognized streams.
<6 The gronP of meteor radiants in Taurus and Aries is complex and of
relatively low activity. Consequently, the hourly rate from this rcgum
has not been investigated systematically and little is known about ny
annual variations in activity which may be present. The total internal
of the shower is generally recognized as extending for nearly a month
from October 26 to November 22, with the hourly rate reaching 10 to 20
over the broad maximum of November 3-10, although Denn.ngH lists
the activity of the group as extending from October to December a.
The radio-echo observationsft can only resolve the total activity, includ-
ing the sporadic meteors, from this region of sky, but no sigmfican
variations have been detected since 1946-the maximum hourly rates
being 18 (1946 November 9), 9 (1947 November 6), 14 (1950 November 9).
The photographic analysis of Miss Wright and Whipple» has enabled
the activity of the various sub-showers to be isolated, and Fig. 146 shows
the frequency of occurrence per 100 hours of exposure of meteors m the
southern and northern Taurid streams (see below). The hourly rate of
the southern Taurids rises abruptly to a maximum at the beginning ol
November (© = 218°) and is followed by a slow decline to late Nov ember,
t Knopf, O., Aslr. Nachr. 242 (1931), 161.
t HofTmeister, C., Die Meteore (Leipzig, 1937), p. 46.
§ Whipple, F. L., Proc. Amer. Phil. Soc. 83 (1940), 711.
|| Denning, W. F., J. Brit. Astr. Assoc. 38 (1928), 302
tf Hawkins, G. S., and Almond, M., Mon. *ot. Roy. Astr. Soc. 1J 2 (^62,219.
XX Wright, F. W., and Whipple, F. L., Tech. Rep. Harv. Coll. Obs. (1950), no. 6
(Harvard Reprint Series 11-35).
298
THE MAJOR METEOR SHOWERS—III
XV, §2
with a secondary maximum around November 11 (© = 228°). On the
other hand, the northern Taurids show only a flat maximum in the
middle of November. Miss Wright and Whipple suggest that the more
concentrated southern Taurid stream may have developed more recently
than the diffuse northern stream.
Fia. 146. Hourly rato of tho southern and northern Taurid meteor streams
according to Miss Wright and Whipple.
— •-• — Southern Taurid stream. — x — x Northern Taurid stream
(c) Radiants
The complex nature of the activity in Taurus was recognized by
Denning,t who in 1928 published a list of thirteen active centres as
given in Table 106.
Table 106
Denning's 1928 List of the Radiants in Taurus and Aries
Streams
Extent of activity
Mean radiant
a 8
{deg.) ( deg .)
1. 0-Arietids .
Oct.-Nov.
21-6
+ 21-9
2. {-Ariotids .
Sept.-Oct.
30*9
9-6
3. a-Arietids .
Sept.-Nov.
320
18-6
4. 39 Arietids .
Aug.-Oct.
40-5
30-9
5. c-Arietids .
Oct.
41-9
13-7
6 . «-Arietids .
Oct.-Nov.
41-9
21-4
7. {-Arietids .
Oct.-Nov.
49-3
18-7
8 . A-Taurids .
Oct.-Nov.
55-7
14-2
9. c-Taurids .
Oct.-Nov.
55-9
9-0
10. {-Taurids .
Nov. 1-17
60-1
28-9
11. y-Taurids .
Oct.-Nov.
61-44
11*8
12. x-Taurids .
Oct. 17-Dec. 1
63-6
22-3
13. {-Taurids . |
Nov. 14-Dec. 16
80-5
23-3
| Denning, W. F., J. Brit. Astr. Assoc. 38 (1928), 302.
XV 5 2 PERMANENT STREAMS OF SEPT. TO DEC.
Denning's remarks on these streams
»*«»■% ^ **- «“ *»>-
sxrr r -— *-*
Taurids, as listed in Table 107.
Table 107
Whipple's First List of seven Photographic Taurid Radiants
Harvard
number
DaU
Corrected radiant
a 5
697
1937 Oct. 31*3507
51°
5"
14°
O'
705
1
1937 Nov. 5*3620
52
56
14
23
1937 Nov. 8*1968
55
12
15
4
710
1937 Nov. 8*2176
54
59
15
1
712
1937 Nov. 10*2343
55
58
15
25
716
1937 Nov. 10-3842
56
10
14
49
719
1937 Nov. 22-046
64
1
15
56
778
1938 Oct. 26*3397
46
53
20
3
In comparing this list with Denning’s radiants (Table 106) it is
evident that one of Denning’s chief radiants (A-Taurids) represen¬
ted in Table 107 (No, 697, 705, 710, 712, 716). Abo No. 778 won Id
appear to be associated with Denning’s e-Ariet.ds. Whipple also
suggested that a meteor previously analysed (No. 642) and classed as
sporadic,§ with a radiant of a 41-9“, 8 +18-7*. could more realistically
be rolated to Denning’s o-Arietid radiant. . ,
By far the most detailed analysis of the radiant structure is that carried
out by Miss Wright and Whipple.* They analysed 102 meteors found
on the Harvard photographic plates between 1896 and 1948 covering
the period October 15-December 2. Ninety of these were single-station
photographs and 12 double station. From this analysis they conclude
that the major activity (49 meteors) is due to a subcentre which they
call the southern Taurid stream, together with the northern Taurid
stream (24 meteors), displaced 7° north of the southern Taurids but with
a similar movement in right ascension. They also isolate two less active
subcentres in Aries—the southern Arietids (or o-Arietids) (8 meteors)
and the northern Arietids (4 meteors) related to the respective Taurid
t Whipple, F. L., Proc. Amer. Phil. Soc. 83 (1940), 711.
X Wright, F. W., and Whipple, F. L. (1950), loc. cit.
§ See Chap. XI.
300 THE MAJOR METEOR SHOWERS—III XV, § 2
streams. There is some doubt as to whether the southern Arietids may
not form a continuous stream with the southern Taurids. Therefore Miss
Wright and Whipple also give a solution whereby both are combined
into one moving radiant. The final solutions for the coordinates of
these various streams are given in Table 108.
Table 108
The Radiants in Taurus and Aries according to the Photographic
Analysis of Miss Wright and Whipple
Southern
Taurid-Arietid
stream
Southern
Taurids
Northern
Taurids
Southern
Arietids
Year and equinox
19500
1950*0
1950*0
1950*0
1950*0
Longitude of sun
223*26°
225*70°
227*74°
206*24°
227*26°
Mean date U.T.
1950 .
Nov. 6*26
Nov. 8*69
Nov. 10*72
Oct. 20*22
Nov. 10*24
Radiant at \ a
53° 19'
55° 13'
56° 55'
41° 38'
41° 20'
moan date j 5
+ 14° 09'
+ 14° 29'
+ 22° 25'
+ 10° 19'
+ 19° 52'
AacosS per day
+ 39'±1
+ 35'±1
+ 28'±1
• •
• •
A8 per day
+ 8'±1
+5'±1
+ 8'±2
• •
• •
Total motion per
day . . ,
40'
35'
29'
• •
• •
Table 109
Predicted Mean Radiant with Date for the Taurid-Arietid Streams
according to Miss Wright and Whipple
(Epoch 1950 0)
Longitude
of sun
Right ascension
Declination
Southern
Taurid-
Arietids
Southern
Taurids
Northern
Taurids
Southern
Taurid-
Arietids
Southern
Taurids
Northern
Taurids
deg.
deg.
min.
deg.
min.
deg.
min.
deg.
min.
deg.
min.
deg.
min.
Oct. 17
203
39
63
,
.
44
35
+ 11
22
•
i
+ 19
01
20
206
41
61
•
.
46
04
11
49
•
•
19
29
23
209
43
60
.
.
47
33
12
16
•
•
19
65
26
212
45
49
46
56
49
01
12
41
+ 13
24
20
22
29
215
47
48
48
45
60
31
13
06
13
39
20
47
Nov. 1
218
49
48
60
33
52
02
13
29
13
64
21
11
4
221
61
49
52
22
63
33
13
62
14
08
21
35
7
224
63
49
64
11
65
04
14
14
14
21
21
67
10
227
55
60
56
01
66
38
14
34
14
34
22
19
13
230
67
62
67
60
68
08
14
64
14
45
22
40
16
233
59
54
69
40
59
41
16
13
14
66
23
00
19
236
61
66
61
30
61
14
15
30
16
06
23
20
22
239
63
58
63
20
62
48
15
47
16
16
23
38
25
242
66
01
65
10
64
22
16
02
16
23
23
65
28
245
E3
67
00
65
67
16
16
16
30
24
12
Doc. 1
248
fee
fel
•
•
67
32
•
•
•
•
24
27
The variation of predicted mean radiant position with date is given
in Table 109. This is shown graphically in Fig. 147 for the northern and
XV, §2
PERMANENT STREAMS OF SEPT. TO DEC.
301
_i-1—
4?' 46' 43'
sy W ST' If Si' S4' S3- St'
Right Ascension a
—aas"•
Fio. 148. Mean radiant paths for the combined southern Taurid-Ariet.d streams
compared with those of the southern Taurid stream, according to the photographic
analysis of Miss Wright and Whipple.
southern Taurid streams in which the individual meteor radiants are
also plotted. Fig. 148 gives similar data for the combined southern
Taurid-Arietid stream with the southern Taurids shown for comparison.
302
THE MAJOR METEOR SHOWERS—III
XV, §2
(d) Velocities
Porterf has analysed twenty-eight possible Taurids between the limits
of November 2 and 19 from the British visual meteor data. The mean
velocity is given as 25-7 km./sec. However, in view of the complexity of
the radiants revealed by Miss Wright and Whipple ,% and of their precise
photographic determination of the velocities, no point would be served
in discussing the details of the visual measurements.
Table 110
Velocities of the Taurids and Arietids according to Miss Wright
and Whipple
Southern Taurid*
Southern
Arielid
Northern Taurid*
Meteor
number .
697
705
710
712
1527
642
778
1009
789
Date.
1937
1937
1937
1937
1947
1936
1938
1940
1938
Oct.
Nov.
Nov.
Nov.
Nov.
Oot.
Oot.
Nov.
Nov.
31-3507
5 3594
82072
10-2343
15 372
21-2972
26 3397
3-3126
15-2607
Corrected la*
61-27
6317
55 27
66-16
58 65
42-29
47-4
68-36
radiant*/5°
+ 1406
14-43
16 07
15-47
14-38
11-37
206
Lil
23-37
v app. rela¬
tive velocity
km./eec.
•32 1
30-9
30-0
29-2
24-6
30-6
33-3
312
27-6
V no atmo¬
sphere
volocity .
32-9
310
30 8
29-6
269
31-4
33 9
31-7
28-3
v f goocentric
_velocity .
31-2
29-2
284
27-3
24 6
29-5
32-3
29-9
26-2
V holiocen-
trio volocity
37-7
37-8
37-6
37-3
36-6
36 3
37-1
37-1
36-9
• Tho slight discrepancies between theso positions and those givon in Tablo 107 aro tho rosult
of a subsequent re-analysis of the data made by L. Jacchia.
Whipple§ presented the velocities of the seven Taurid meteors which
were listed in Table 107. In the later publication of Miss Wright and
Whipple ,% hve|| of these which were suitable for orbital calculation were
retained, and three more recent doubly photographed meteors added.
In addition, one previously classed as sporadieft (No. 642) has been in¬
cluded as a southern Arietid. The velocity data for these nine accurately
measured meteors are given in Table 110.
The most striking characteristic of these velocities is the marked
decrease in geocentric velocity with increasing solar longitude—a rela¬
tion which appears to be independent of stream association. This feature
t Porter, J. 0., Mon. Not. Roy. Astr. Soc. (1943), loc. cit.; (1944), loo. cit.
x Wright, F. W., and Whipple, F. L., loc. cit.
§ Whipple, F. L. (1940), loc. cit.
|| Theee five (697, 705, 710, 712, 778) were the only ones of the original set completely
photographed with double cameras and rotating shutters,
ft Whipple, F. L., Proc. Amer. Phil. Soc. 79 (1938), 499.
XV, §2
303
PERMANENT STREAMS OF SEPT. TO DEC.
was pointed out by Whipplet and confirmed in the later anatyeis of
Miss Wright and Whipple,! whose results are plotted in tig.
Whipple also pointed out that although the observed velocities varied
over a range of nearly 3-5 km./sec., the heliocentric velocities were almost
constant, with an apparent decrease in time of apparition. Owing to
Fio. 149. Tho relation betwocn tho geocentric velocity (v B ) and tho holiocontric
volooity (V) with dates for thoTaurid-Ariotid showers according to Mias Wright
and Whipplo.
• Southorn Taurida, o Northern Taurids. + Southom Arietids.
the importance of any such variation of heliocentric velocity, Whippief
made a careful investigation of the errors of measurement, and concluded
that it was not possible to make any certain deduction concerning the
reality of this apparent variation of heliocentric velocity with time. Tho
fuller data plotted in Fig. 149 also indicate a possible slight decrease
in heliocentric velocity with time. The changes in the other orbital
elements with date are, however, real, and these will be referred to
below.
(e) Orbits
The orbital data for the nine meteors whose velocities are listed in
Table 110 are tabulated in Table 111. These are taken from the data of
Miss Wright and Whipple.J The results for five of the meteors (697, 705,
710,712,778) were also given earlier by Whipple, t One of the most striking
features of these data is the short period of the orbits, and this immediately
t Whipple, F. L., loc. cit.
x Wright, F. W., and Whipple, F. L., loc. cit.
THE MAJO
O Aft,
4 •« o*
.5 3 t- a n o — ® ® S r?
l. -i « » n fi a o - o I n
S d •»'*««? ? TT 9
w l MNNN- “ N N C
9 9
e> (N
10 - oi»|o
Tf -f C*5 C*J
u? -
-a O’
oa. ? coon *
|»»b‘b^‘0 «o«d« cj
^ s?
!3 I
3 *
CJ
j . 5 c{ .iflCf (ON N 17
"2 v ? r- N IQ r> N r~ <N O M -*
& § 1 S---** " 333 3
o « - >3 h
ontion
N --00
N hO®
<N haMO
OJ © ® CO CO
— MNN -
M3 O N I-
O O « « N
O f- I» o
305
XV § 2 PERMANENT STREAMS OF SEPT. TO DEC.
invites comparison with the ideas of Knopff and Hoffmeister{ that the
Ta’rid stream is of interstellar origin. A comparison of the m^ean
latitude, longitude, and daily motion of the used by K,opf
shows very close agreement with the similar quan 1 le ,
Sid meteors listed in Table 111 , and leaves little room fox-doubtthat
te same streams are under investigation. In the hght of the photographi
measurements, the idea of the interstellar origin for these streams has
therefore to be definitely abandoned, a conclusion later accepted by
Hoffmeister.§
It was mentioned in (d) above that the heliocentric velocities do not
show any marked change with date, but this is not the case for the other
orbital elements. The most conspicuous correlation is that of perihelion
distance q, which increases with date as shown in Fig. 150. a, e, cu, and i
also show systematic variations with time. The aphelion distance q is
not well correlated with date. The longitude of perihelion, shows no
correlation, but its scatter is small within each stream. These changes
f Knopf. 0., loc. cit. X Hoffmcister, C., loc. cifc.
§ Hoffmeister, C., Metcorstr&me, ch. 8.
X
8695.6®
THE MAJOR METEOR SHOWERS—III
XV, §2
306
Fio. 161. Orbits of two southern Taurid meteors. Projection on the
piano of the ecliptic.
No. 697, 1937 Oct. 31, o = 0 88, i - 6-3*.
No. 712, 1937 Nov. 10, e - 0*82, i - 4 6°.
Fio. 152. Orbits of three northern Taurid meteors, compared with the orbit of
Encko's Comet. Projection on the plane of the ecliptic.
in orbital characteristics with date are represented by the orbits drawn
in Figs. 151 and 152. Fig. 151, taken from Whipple,t shows the orbits
of two southern Taurids—697 of October 31 and 712 of November 10.
f Whipple, F. L., loc. cit.
307
xv. §2 PERMANENT STREAMS OF SEPT. TO DEC.
The orbits of the meteors of intermediate date. 705 and 710 ^ ^tween
these two but are omitted for clarity. Fig. 152, t®^® 1
Whipple,t illustrates similarly the progress.on m the-northernJ
In both diagrams the projection is on to the p ane o f ^hpt «.
The planes of the orbits of these Taurid meteors he very close
planes of the orbits of the planets, and Whipple}
approaches with Mercury, Venus, and Mars could occur. Table 11
gives Whipple’s figures for the distance M perpendicular to the ecbpti
between Z meteor and planetary orbits at the t.mes of
vector and heliocentric longitude. (A posrt.ve sign for M indicates
that the meteor passes north of the planetary orbit.)
Table 112
Minimum Distances of Taurid Meteors from Planetary Orbits
Meteor no.
697
705
712
Planet
True anomaly
AZ (a.u.)
AZ (a.u.)
AZ (a.u.)
Mercury .
Venus .
Kurth
Mara
+
+
+
+
-0002
-0016
+ 0038
+ 0052
0 000
-0099
-0018
-0110
-0010
-0008
+ 0032
-0037
0 000
-0072
-0020
-0082
0022
+ 0026
-0026
0000
-0 052
-0019
-0082
The Taurid stream spreads over at least 0-2 a.u. along the echptical
plane, and hence, in view of the smaU values of A Z, it seems that the
shower must be active for aU four planets both before and after perihelion
passage. This consideration led Whipple to make the remarkable
prediction in 1940J that ‘in the case of the earth, the radiant of the post¬
perihelion shower would be in the general direction of the sun, producing
only day-time meteors unlikely to be observed except as fireballs in late
June and early July’. We shaU see later (Chap. XVIII) that the develop¬
ment of the radio-echo techniques led to the detection of this return
shower as one of the prominent summer day-time meteor streams.
In addition to the orbital elements for the Taurid meteors, Table 111
gives the mean elements for Encke’s Comet, the orbit of which is also
shown in Fig. 152, projected on to the plane of the ecliptic together with
the northern Taurid orbits. The similarity between the orbits of the
comet and the meteors is very marked, and strongly suggests that the
comet and the meteors must have a common origin or other close
t Wright, F. W., and Whipple, F .L., loc. cit. t Whipple, F. L., loc. cit.
308
THE MAJOR METEOR SHOWERS—III
XV, §2
connexion. There is, however, a major difficulty in that the plane of the
meteor orbits and of the orbit of Encke’s Comet differ by 10° or 15°.
Whipple f has investigated this discrepancy in considerable detail. He
has shown that the differing inclinations can be explained by the
perturbing effect of Jupiter, and that a common origin for the meteors
and the comet is highly probable. This topic will be considered more
fully in Chapter XXI.
3. The Geminid shower
(а) History
The Geminid meteor shower, which reaches a maximum on December
13-14, provides one of the richest and most reliable meteor displays of
the year. There do not appear to be any records of this shower in
antiquity; in fact, according to King! the existence of the shower was
first recognized in England by R. P. Greg in 1862 and in the United States
by Marsh and Twining in the same year. Denning’s§ general cata¬
logue certainly includes many records of Geminid meteors going back
to 1862, and he claims|| to have established the movement of the radiant
point in 1877. In more recent years Whipple’sft photographic meteor
studies revealed the surprising fact that the orbit of the stream was one
of unusually short period.
(б) Activity
Few systematic visual data of the activity of the Geminid stream are
available—presumably due to the generally unfavourable sky conditions
prevailing in December. The various records of the British visual
observers JJ: indicate that at least during the present century the shower
has yielded a fairly constant hourly rate lying between 20 and 60 at
maximum. A visual-rate curve deduced from information supplied by
Hoffmeister§§ is shown in Fig. 153 (a). Since 1946 the shower has been
observed systematically, using the radio-echo technique. The hourly
rates at maximum for the various years are given in Table 113. The
progress of the shower with date for the years 1949 and 1950 as observed
on the radiant survey equipment|||| with the rates corrected for variation
t Whipple, F. L., loc. cit.
X King, A., Mon. Not. Roy. Aatr. Soc. 86 (1926), 638.
§ Denning, W. F., Mem. Roy. Aatr. Soc. 53 (1899), 203.
|| Denning, W. F., Mon. Not. Roy. Aatr. Soc. 84 (1923), 46.
tt Whipple, F. L., Proc. Amer. Phil. Soc. 91 (1947), 189.
XX Mem. Brit. Aatr. Aaaoc. 1 (1892), et seq.
tt Private information quoted by Hawkins, G. S., and Almond, M., loc. c»t.
HI) Aspinall, A., Clegg, J. A., and Hawkins, G. S., Phil. Mag. 42 (1951), 504 (see
Chap. IV).
Hourly rate
Fia. 153. (a) Hourly rat© of the Gominid stream plotted against sun’s longitude.
• 1949*1 Radio-echo observations corrected for variations in sensitivity of
O 1950/ equipment.
-Visual observations (Hoffmcister).
(6) Hourly rate of the Geminid stream plotted against sun's longitude, accord¬
ing to the radio-echo observations 1946-50 (uncorrected for sensitivity
variations).
(c) Percentage of radio echoes from the Geminid meteors with durations
exceeding 1 second plotted against sun’s longitude.
310
THE MAJOR METEOR SHOWERS—III
XV, §3
Table 113
Activity of the Geminid Meteor Shower as observed by the
Radio-echo Technique
Longitude of sun
at maximum ©
Date of maximum
Hourly rate
at maximum
deg.
201-4
1946 Dec. 14
63
201-3
1947 Dec. 14
67
2611
1948 Dec. 13
60
200-8-201-8
1949 Deo. 13-14
81
260-6
1950 Dec. 13
79
201-3
1951 Dec. 14
75
200-0
1952 Dec. 12
72
260-7
1053 Dec. 13
71
in sensitivity of the apparatus is plotted in Fig. 153(a), while 153(6)
summarizes all the uncorrected information for the years 1946-50 in¬
clusive. It seems evident from these data that the shower may be con¬
sidered to have an almost constant activity from year to year. Also it
appears that the stream density is asymmetrical about the maximum,
the Earth encountering less debris after maximum than before. There
is some indication that this asymmetry does not extend throughout all
mass groups. For example, in Fig. 153(c) the hourly rate curves for
long-duration and short-duration echoes are compared. It is known that
the long-duration echoes are associated with larger meteors than the
short-duration echoes,t and hence it seems that the smaller meteors in
the Geminid stream may be distributed fairly symmetrically around
O = 259°.
(c) Radiant
The general catalogue of Denningt contains many determinations of
the Geminid radiant. In 1923§ Denning stated that he first obtained
convincing evidence of the motion of the radiant in 1885. The summary
of the radiant ephemeris given by Denning in 1923 agrees closely with
the mean ephemeris computed by King|| in 1926 for the visual observa¬
tions which were then available. However, Maltzevff criticized the
ephemeris given by King on the grounds that his treatment of the basic
data was inadequate. The two ephemerides, both deduced from the same
observational data, are given in Table 114.
t Greenhow, J. S., and Hawkins, G. S., Nature, 170 (1952), 355.
t Denning, W. F., Mem. Roy. Astr. Soc. (1899), loc. cit.
§ Denning, W. F., Mon. Not. Roy. Astr. Soc. 84 (1923), 40.
|| King, A., ibid. 86 (1926), 038.
ft Maltzev, V. A., Rum. Astr. J. 8 (1931), 67.
XV, § 3 PERMANENT STREAMS OF SEPT. TO DEC
Table 114
Of m « -* %»*** %
Maltzev in 1931 from Visual Observations
311
Subsequent visual ODscrvauu..* — ' - nn^itions
Americans observers have shown general agreement with the pos.t.ons
8 'Whippl^hM'carried out a precise investigation of the Gcmiwd
radiant from the collected Harvard photographic data. Frn, double-
station photographs obtained in 1936 and 1937 yielded the indiv dual
radiant data listed in Table 116. An additional thmty-six single trails
photographed between 1903 and 1945 were used, after the application
of special corrections, to give the mean radiant andda.lymot.on bsted
in Table 116. These results are in close accord with the visual da
referred to above.
Table 115
Whipple's Photographic Determinations of the Geminid Radiant from
Meteor no.
Date
Apparent radiant
a (1900) 5(1900)
Corrected radiant
a (1900) 8 (1900)
727
730
733
736
651
1937 Dec. 12-3774
1937 Dec. 13-3256
1937 Doc. 13-4254
1937 Dec. 14-3796
1936 Dec. 14-3077
112° 12' +33° 00'
112° 41' +32° 53'
112° 49' +33° 28'
113° 16' +32° 47'
113° 15' +32° 20'
110° 56' +32° 29'
111° 46' +32° 33'
111 0 29' +32° 49'
112° 00' +32° 15'
112° 26' +32° 02'
t Hoffmeister, C., Meleorstrome (Weimar, 1948).
t Mem. Brit. Aslr. Assoc. 32 (1936).
S Olivier, C. P., Publ. McCormick Obs. 5 (pt. i), 19-9.
|| Whipple, F. L., Proc. Amer. Phil. Soc. 91 (1947), 189.
312
XV. §3
THE MAJOR METEOR SHOWERS—III
Table 116
Whipple's Determination of the Daily Motion of the Oeminid Radiant
from Thirty-six Single and Five Doubly Photographed Trails
Apparent radiant
Corrected radiant
Year and equinox
1900 0
19450
1900-0
1945-0
Mean solar longitude .
260-34
260-97
260-34
260-97
Mean date U.T. (Dec.)
12-31 d.*
13-35d.
12-31 d.*
13-35d.
Mean a
111° 54'
112° 38'
110° 27'
112° IP
Mean 8
+ 32° 56'
+ 32° 50'
+ 32° 30'
+ 32° 25'
Aa per day
+ 63'
+ 63'
+ 63'
+ 63'
AS per day
+ 3'
+ 3'
-4'
-4'
Total motion per day .
53'
53'
53'
53'
• G.M.T.
The radio-echo observations summarized by Hawkins and Miss
Almondf are also in good agreement with the visual and photographic
data. The data for the 1949$, 1950,$ 1951,$ and 1952$ observations
are given in Table 117.
Table 117
Radio-echo Observations of the Geminid Radiant Position
1949
1950
1951
1952
Solar
Solar
1
Solar
n
Solar
longitude
Radiant
longitude
Radiant
longitude
Radiant
longitude
Radiant
Date
O
a
5
©
a
5
o
a
s
O
a
8
deg.
deg. deg.
deg.
deg. deg.
deg.
deg. deg.
deg.
deg. deg.
Dec. 7
• .
• •
••
264 4
107 +37
• «
• •
• •
• .
. ,
8
255-7
108 +33
266-4
101
31
• •
• •
• •
. .
, #
0
256-7
108
36
256-4
108
30
256-2
110
36
256-9
110
32
10
257-7
110
36
257-4
108
32
257-2
112
36
257-9
111
33
11
258-8
110
30
258 6
111
32
• «
• «
• a
112
31
12
259-8
111
32
259-5
112
32
259-2
111
31
260-0
113
31
13
260-8
112
30
260-5
113
30
260-2
113
31
261-0
114
32
14
261-8
115
33
261-6
115
31
261-3
116
36
262-0
116
32
15
262-8
114
34
••
••
••
262-3
114
29
• •
••
• •
The daily movement of the radiant point as determined by the visual,
photographic, and radio studies is in close agreement, as indicated in
Table 118.
Table 118
Daily Motion of the Geminid Radiant
a 8
Radio echof
Photographic!
Visual (King)||
(Maltzev)tf
+ l-3°±0-l°
+ 105°
+ 1 - 2 °
+ 1 - 0 °
-0-3°±0-l°
- 0 - 66 °
- 0 - 1 °
- 01 °
f Hawkins, G. S., and Almond, M., loc. cit.
j Jodrell Bank unpublished. § Whipple, F. L. (1947), loc. cit.
|| King, A., loc. cit. tt Maltzev, V. A., loc. cit.
313
XV. §3 PERMANENT STREAMS OF SEPT. TO DEC.
There are, however, surprising discrepancies in the measurements o f
the radiant diameter given by the three techniques. The radio observ -
tions indicate a radiant diameter not greater than 4 ; the visual obse
tions indicate a diameter of about 12° with a concentration m a reg on
4° X 3° around the mean position^ From a detailed investigation ot the
photographic trails Whipplet found the random probable error ol the
radiant point of a Geminid to be ±21'. In view of the.mportanceo
ascertaining whether this represented a true cosmic spread m the spatial
motions of the Geminid meteors as they approached the earth, Whipple
investigated four other possible causes:
(i) Measuring error, which was found to contribute ±2' at most to
the spread. . ,
(ii) Errors in zenith correction arising from uncertain radiant ami
time of apparition. These are unlikely to introduce errors of more
than 3' (corresponding to a degree error in the radiant position)
or ±8' due to uncertain time of apparition.
(iii) Deviations from linear motion in the atmosphere. A deviation
of 20' perpendicular to the trail would correspond to 60 microns
per centimetre departure from linearity on the plate, whereas the
average departure is only a few microns.
(iv) Spread in radiant arising from the combination of observations
made in different years or nights. In this case the meteors
observed in one night or in one year should show a smaller
deviation from the mean radiant than ±21'. Fig. 154 shows the
extended corrected trails of single-station Geminids and the
radiants of double-station Geminids photographed in 1937, while
Fig. 155 shows the single-station trails of 1938 December 14. It is
evident from these figures that the Geminid meteors of a single
year show random deviations of the same order as those observed
in different years.
The conclusion from Whipple’s investigation is that an actual cosmic
spread of the order of ±20' does exist in the Geminid meteors. As an
explanation Whipple favours the idea that such a spread arises because
of planetary perturbations. These introduce random effects because of
the differing positions, and subsequently the differing orbital paths of
the individual particles. Whipple makes the further interesting point
that a full theory would provide some measure of the age of the Geminid
stream. For example, effects due to light pressure§ and related electro-
f Prentice, J. P. M., private communication.
x Whipple, F. L. (1947), loc. cit. § See Chap. XX.
314
THE MAJOR METEOR SHOWERS—III
XV, §3
magnetic effects are inadequate to produce finite deviations over intervals
of less than hundreds of thousands of years on meteors with diameters of
a centimetre.
Fio. 154. Extended corrected trails and double-station radiants
of photographic Geminids recorded in 1937.
(The notation is the Harvard plate numbering.)
R — mean calculated radiant.
- — extended single trails. O — doublo-station meteor radiants
Fio. 155. The single-station trails of Geminids
photographed on 1938 Dec. 14.
(The notation is the Harvard plate numbering.)
315
XV §3 PERMANENT STREAMS OF SEPT. TO DEC.
' The significance of the much greater spread found in ther^eeho
and visuS work is not yet apparent. It may well be conne ted w th ho
differing samples of mass groups observed m the various techiuq .
Geminid velocities are not represented in the coUect.on of Bnt,
meteor data presented by Porter, t MaltzevJ lists n^^mnudsobse^ed
by Denning between 1892 and 1915 and three observed by Olmer in 1923
bit in view of the subsequent preeision photograpkc and raio-echo
measurements no purpose would be served in (hscussmg these visual
observations.
Table 119
Photographic Determinations of the Velocities of Geminid Meteors
WHIPrLK§
Harvard meteor
number
Date . •
727
1937 Dec.
12-3774
730
1937 Doc.
13 3256
733
1937 Doc.
13 4254
736
J937 Doc.
14-3796
651
1936 Dec.
14-3077
v Apparent rela-
tivo volocity
(km./sec.)
35-21
35-96
38-26
36-05
36-56
V No atmo¬
sphere velo¬
city (km./soc.)
35-62
3662
38-44
36 31
36-81
v g Gcocontrio
volocity (km./
6ec.)
34-01
34-97
37 04
34-74
35-14
V Heliocentric
velocity (km./
sec.) .
33-46
34-16
3567
34-39
34-53
§ Whipple, F. L. (1947), loc. cit.
Harvard moteor number
Date . . • • •
v Apparent relative velocity
(km./soc.)
jacchia||
1112
1265
1941 Dec. 11-27
1944 Dec. 14-22
36-64
35-95
1539
1947 Dec. 14-20
35-661,.
35-53/ 11
Jacchia, L. G.. Tech. Rep. Harv. Coll. Obs. (1948). no. 2 (Harvard Reprint Series
H-26).
tt Corresponding to two heights of the trail. 67-3 and 65-4 km. respectively.
Eight values for the velocity of Geminid meteors determined by the
double-camera photographic technique have been published. Complete
t Porter, J. G., Mon. Not. Roy. Astr. Soc. 103 (1943), 134; 104 (1944), 257.
x Maltzev, V. A., loc. cit.
316
THE MAJOR METEOR SHOWERS—III
XV, §3
details for five have been given by Whipplef and values for the apparent
relative velocity for three others by Jacchia.t as listed in Table 119.
Omitting no. 733 for which the determinations of all elements showed
appreciable divergence, Whipple gives mean values for nos. 727, 730,
736, 651 as follows:
Dec. 13-6
v = 35-95 km./sec.
V = 36-34
v, = 34-72 „
V = 34-14
Measurements of the Geminid velocities by the radio-echo technique
have been made in Great Britain and Canada. Preliminary British
measurements, using the pulse diffraction technique§ in 1948 have been
described by Ellyett and Davies.|| More comprehensive measurements
were made in 1949, when 122 velocities were obtained between December
9 and 15. These have been described in Chapter XII. Fig. 106 shows the
histogram of the results, and the discussion on pp. 218, 219 showed that
there must be a true spread in the Geminid velocities. A further 149 veloci¬
ties measured in 1951 December gave similar results.tt
An attempt to estimate the actual spread in heliocentric velocities
was made by Hawkins and Miss AlmondJt using the same treatment as
for the Quadrantids and Perseids. They combined the 1948 and 1949
measurements, and, with the same notation, found
o R = 1-2 km./sec., o 3 = 3-5 km./sec., a K = 1-5 km./sec.,
a A = 0-3 km./sec., o 0 = 4-6 km./sec., and hence o H = 2-3 km./sec.
This spread is considerably greater than the equivalent standard devia¬
tion of 0-23 km./sec. found in the photographic measurements. The
reason for the difference is not known, but is presumably introduced
because of the wide difference in range of mass groups covered by the
photographic and radio techniques.
The Canadian measurements§§ were made by using the continuous-
wave diffraction technique and non-directional aerial systems. The
results, and McKinley’s method of analysis, have been described in
Chapter XII in connexion with the distribution of sporadic velocities.
The mean apparent observed velocity was 35-25 km./sec. Corrections
t Whipplo, F. L. (1947), loc. cit.
X Jacchia, L. G., Tech. Rep. Harv. CM. Obs. (1948), no. 2 (Harvard Reprint Series,
II-26). § See Chap. IV.
|| Ellyett, C. D., and Davies, J. G., Nature, 161 (1948), 696.
tf Jodrell Bank, unpublished. XX Hawkins, G. S., and Almond, M., loc. cit.
§§ McKinley, D. W. R., Astrophys. J. 113 (1951), 225.
XV, §3 PERMANENT STREAMS OF SEPT. TO DEC. 317
for diurnal motion, zenith attraction, and deceleration gave the corrected
geocentric velocity v g = 34-2 km./sec., compared with the 34-72 km./se .
of Whipple’s photographic measurements.
Taking into consideration the different mass groups covered by the
various techniques, it is evident that the three determinations of the
velocity of the Geminid meteors are in excellent agreement.
(e) Orbit . .... ,
In 1931 Maltzevf speculated on the orbit of the Geminids Although
handicapped by lack of knowledge of the precise velocities he brought
forward arguments in support of the view that the orbit must be elliptical,
an opinion which has been confirmed by recent work. The surprising
nature of the ellipticity of the Geminid orbit was not revealed until the
publication of Whipple’s photographic measurements in 1947.; His
results on the radiants and velocities of five doubly photographed meteors
have been quoted above, and Table 120 gives the corresponding orbital
data. Hawkins and Miss Almond§ have also computed a mean orbit
from the radio-echo data, and these elements are included in Table 120
for comparison.
Table 120
Orbital Elements for the Geminid Meteors
Mftfori
Harvard
No. 727 .
Harvard
No. 730 .
Harvard
No. 733 .
Harvard
No. 730 .
Harvard
No. 651 .
Mean (omit¬
ting No.
733).
Mean radio
echo un¬
co rrected .
Mean radio
echo cor¬
rected for
decelera¬
tion .
J)aU ft (1000 0) _
• »•*•'•' fl.M.
259 25 325 01 -24 57 23 04 1-302
10t7 l)cc
13-3256’ 260 22 324 44 -21 58 24 27 1-399
1937 Dec.
13- 4254 260 29 324 25 -16 04 27 26 1 678
l ??3796 261 27 323 28 - 21 17 23 00 1-434
1936 Dec.
14- 3077 261 37 324 04 -20 34 23 20 1-457
a.u.
0-1398 0-893
0-1360 0-903
0-1270 0-924
0 1434 0-900
0 1380 0-905
Dec. 13-6 260 43 324 19 - 22 12 23 28 1-390 0-1393 0 900 1 05
1948 Dec. 261-1 ±0-5 325 ±2
1948 Dec. 1261-1 325
23 ±3 11-31 ± 04 0 14 ± 02 0 89 ± 01 1-50
•23 1-4 0 14 0 89 1 60
The orbits of the photographic meteors are drawn in Fig. 156 projected
on to the plane of the ecliptic. Fig. 157 shows Whipple s mean orbit,
t Maltzev, V. A., Russ. Aslr. J. 8 (1931), 67.
x Whipple, F. L. (1947), loc. cit.
§ Hawkins, G. S., and Almond, M. f loc. cit.
318
THE MAJOR METEOR SHOWERS—III
XV, §3
together with the mean radio-echo orbit computed by Hawkins and
Miss Almond. It is evident from Table 120 and from Figs. 156,157, that
Fio. 156. Projection on the ecliptic of the Gerainid orbits determined by tho
photographic technique. Tho notation corresponds to Table 120.
Fio. 157. Tho orbits of Geminid meteors projected on to the plane of the ecliptic.
- Mean orbit computed from the radio-echo observations.-Mean
orbit given by Whipple from the photographic observations.
very close agreement exists between the photographic and radio-echo
orbits. These orbits are unique compared with the orbits of known
comets, planets, or asteroids. The shortest-period comet known (Encke’s)
319
XV, §3
PERMANENT STREAMS OF SEPT. TO DEC.
has aperiod of 3-3 years, or twice the mean period of these Gemrnid orb -
This topic will be discussed again in Chapter XXI, but there is no certam
solution of the possible origin of such short-period meteor orbits.
4. The December Ursids (BeSvar’s stream)
(a) History c ,
At 16h. 30m. U.T. on the afternoon of 1945 December 22 one of the
observers at the SkalnaW Pleso observatory in Czechoslovakia noticed
a very high meteor frequency, and observation in the succeeding hours
showed that an unexpected meteoric display was taking place. 1 he event
was reported by Beivaf ,t who placed the radiant in Ursa Minor and gave
the hourly rate as 169. Bc6v4fJ again reported the return of the shower on
1946 December 22, but this time gave the hourly rate as 11. This shower
was seen visually in England by Prentice§ in 1947 and was also located
by the radio-echo technique.|| Since that time the shower has been
studied systematically by the radio-echo technique, but the hourly rate
has never oxceeded 15 to 20. In retrospect it appears possible that thiB is
the same minor stream established by Denningtt from his observations
between 1890 and 1910, and that the spectacular stream observed by
BefivAr in 1945 may represent a condensation in the orbit or be related
to it in some other manner.
(b) Activity
BeSvdrf originally gave the hourly rate of the stream on the night of
its discovery in 1945 as 169; but in a more recent analysis of the original
data CeplechaJt states that this was the total frequency seen by four
observers.§§ The true zenithal rates given by Ceplccha, as the mean of
three observers, are listed in Table 121 for the period 16h. 50m., just after
it was firstobserved, to 18h. 20m., when clouds and the moon stopped the
observations. The mean rate over the 100 minutes of observation was
48 per hour.
As mentioned above, this high rate has not been encountered in
subsequent years, the data for which are given in Table 122, the hourly
rate being the maximum observed in all cases.
t Bofivdf, A., I.A.U. Circular, no. 1026, Jan. 24, 1946.
j BoCvdf, A., ibid., no. 1078, Feb. 4, 1947.
§ Prentice, J. P. M., J. Brit. Astr. Assoc. 58 (1948), 140.
|| Clogg, J. A., Hughes, V. A., and Lovell, A. C. B., ibid., p. 134.
tf Donning, W. F., Brit. Astr. Assoc. Observers Handbook (1922), p. 15.
XX Ceplecha, Z., Bull. Cent. Astr. Inst. Czech. 11 (1951), 156.
§§ It should, perhaps, be mentioned that Becvar. having been deposed from office,
has had no opportunity of replying to these and other criticisms of his observations.
320
THE MAJOR METEOR SHOWERS—III
XV, §4
Table 121
Hourly Rates of the Betovar Meteor Stream , 1945 December 22
Time U.T.
Hourly rate
Time U.T.
Hourly rate
16h. 50m.
36
17h. 40m.
26
17 00
20
17 50
66
17 10
69
18 00
108
17 20
34
18 10
38
17 30
14
18 20
101
Table 122
Hourly Rate of the Ursid Stream subsequent to 1945
Source
Technique
Time of maximum
O at max.
Maximum
hourly rate
Beivfif t and CeplochaJ
Visual
1946 Dec. 22
270° 62'
11
Prentico§
Visual
1947 Dec.
270° 30'
20
Clegg, Hughes, and
15
LoveU||
Radio-echo
1947 Dec. 22
270° 0'
Clegg, Lovell, and
269° 23'
16
Prenticoft •
Radio-echo
1948 Dec. 21d. 08h.
Hawkins and Al-
270° 12'
13
mondtJ
Radio-echo
1949 Dec. 22d. 07h. 20m.
Hawkins and Al-
269° 48'
20
mond§§
/
Radio-echo
1950 Dec. 22
Radio-echo
1951 Dec. 23
270° 30'
13
Jodroll Bank, unpub-1
Radio-echo
1952 Dec. 22
270° 24'
9
lished y
Radio-echo
1953 Dec. 23
271°
11
BeSv&f mi originally reported the stream to be of short duration, 4 hours
only, but in the recent analysis Ceplechat makes it clear that this short
duration was determined by twilight on the one hand and moon and
clouds after 18h. 20m. on 1945 December 22 on the other, and that the
duration of the stream was probably much greater than 4 hours. The radio¬
echo observations in the years 1947 to 1953 have shown that the duration
of the Ursid stream is, in fact, some 30 to 40 hours. A typical example of
the trend of the activity of the stream is given in Fig. 158, this being the
plot of the hourly rates of the stream and of the accompanying sporadic
t BeSv&f, A. (1947), loc. cit.
X Ceplecha, Z., Bull. Cent. Astr. Inst. Czech. II (1951), 156.
§ Prentice, J. P. M. (1948), loc. cit. .
|| Clegg, J. A., Hughes, V. A., and Lovell, A. C. B. (1948), loc.jcit. 9 _
tt Clegg, J. A., Lovell, A. C. B., and Prentice, J. P. M., J. Bnt. Astr. Assoc. 60 (1949), 27.
XX Hawkins, G. S., and Almond, M., ibid. 60 (1950), 251.
§§ Hawkins, G. S., and Almond, M., Mon. Not. Roy. Astr. Soc. 112 (1952), 219.
HD Be6v«, A. (1946), loc. cit.
321
XV, §4 PERMANENT STREAMS OF SEPT. TO DEC.
activity for the radio-echo observations of 1949 December f Inthis case
the stream was active for 34 hours between © 269-5° and 271-3 wl °“ a
maximum at© = 270-2°. The results for the year 1947,1948,1950,1961,
and 1952 are very similar.
Fio. 158. Tho activity of the December Ureids as recorded by the radio-echo
technique in 1949. The broken line is the smoothed hourly rate. Tho lower
curve shows tho hourly rate of sporadic meteors (thoso with range-time plots
outside tho theoretical onvelope). A marks the influence of tho apex
component.
(c) Radiant
The radiant position quoted by BeCvaf in his original announcement
was a 233°, 8 + 82-6°. This position was markedly different from all
subsequent visual and radio-echo determinations, and Ceplechat has
recently investigated the original data. During the progress of the
shower, three meteors were recorded photographically and Ceplecha s
reduction of these gives the following coordinates
o (1946) 8 (1946)
216° 53' 75° 48'
217° 12' 75° 55'
219° 27' 75° 16'
The weighted mean, corrected for diurnal aberration and zenithal
attraction, is
a (1950) = 217° 05'±4'; 8 (1950) = +75° 51'±3'
on 1945 December 22-773±0-051 U.T.
This differs widely from the position given by Becvar which was obtained
from sixteen meteors plotted by Dzubak. Fortunately, two of these
plotted meteors were also photographed, and it became evident that the
systematic errors in the visual data fully accounted for the difference
f Hawkins, G. S., and Almond, M. (1950), loc. cit.
X Ceplecha, Z. (1951), loc. cit.
Y
3695.66
322
THE MAJOR METEOR SHOWERS—III
XV, §4
in the visual and photographic positions. The correct position of the
1945 radiant is therefore the one given by Ceplecha and not the original
position quoted by Befiv&r. Radiant positions from visual observations
have also been obtained by BochniSekt and by Van^sekJ in 1946, and
by Prentice§ in 1947. These are listed in Table 123 together with the
radio-echo determinations of the radiant coordinates. The low hourly
rate and high declination make determination of the radiant coordinates
difficult by the radio-echo technique, and the limits of error quoted in
Table 123 are therefore large.
Table 123
Radiant Positions of the Ursid Meteor Stream
Whether cor¬
rected for diur¬
nal aberration
Radiant
and zenithal
Source
Technique
Date
a
s
attraction
Ceplecho|| .
Photographic
1946 Dec. 22-773
217* 06'±4' + 76°61'±3'
Yes
Boohnifiokt, tt •
Visual
1946 Dec. 22-9
213*±4
+ 76 ± 1
Yea
VanfsckJ .
Visual
1946 Deo. 22-9
217-8*±08°
+ 76-7*±l*
Yea
Prontico§ .
Visual
1947 Dec. 23-16
207*
+ 74°
No
Clogg, Hughes,
and Lovollii .
Radio-ocho
1947 Dec. 22 23
195*±8*
+ 78* ±6*
No
Clogg, Lovell,
and Prontico§§ .
Radio-echo
1948 Dec. 20-23
210*±10“
+ 82*±8»
No
Hawkins and
+ 77-6*±3°
Yes
Mina AlmondHH.
Radio-ocho
1949 Dec. 22
207-1* ±8°
Hawkins and
Miss Almondttt
. _ . /
Radio echo
1960 Dec. 22
199* ±8°
+ 77*±3*
No
Radioecho
1961 Dec. 23
) =£= 200°
^ +77*
1 No
Jodrell Bank
Radio ocho
1962 Dec. 22
[ Rate too low for accurate
(unpublished) 1
Radio-echo
1953 Dec. 23
) determination
)
Considering the limits of error of the radio-echo determinations, the
agreement amongst these observations is satisfactory. The most serious
discrepancy occurs in the declination measurement for 1948, but Hawkins
and Miss Almond|||| have pointed out that this need not be considered
significant since there was a gap in the observations at the critical period
of the shower which probably gave rise to a false value for O m ax an< *
may have interfered with the coordinate measurements.
t Bochnliek, Z., Bull. Cent. Astr. Inst. Czech. 1 (1948), 26.
1 Vanfoek, V., ibid. 1 (1947), 10. ...... , ..
§ Prentice, J. P. M. (1948), loc. cit. II ? 6 P l6c 1 h n a ; a Z ’ J, ,
tt Unfortunately, in the original announcement of the 1946 results Betvhr (I.A.U.
Cxrc. 1078) quoted the right ascension as 203° instead of 213°.
XX Clegg, J. A., Hughes, V. A., and Lovell, A. C. B. (1948) c,t '
§§ Clegg, J. A., Lovell, A. C. B., and Prentice, J. P. M. (1949), loc. cit.
DU Hawkins, G. S., and Almond, M. (1960), loc. cit.
tft Hawkins, G. S., and Almond, M. (1962), loc. cit.
XV, §4
PERMANENT STREAMS OF SEPT. TO DEC.
323
(< d ) Velocities . .
There are no published records of visual or photographic: determui -
tions of the velocities of meteors in the Ursid stream. Attempts to
measure the velocities by the radio-echo technique have been made, in
each year, but owing to the low hourly rate only partial success has been
Velocity (km/see.)
Fxo. 169. Distribution of velocities measured during the opoch of the
1951 Ursids.
achieved. The velocities of three possible Ursid meteors were measured
in 1948 as follows:!
1948 Dec. 21d. 19h. 20m. 52s. 39-5±4-8 km./sec.;
1948 Dec. 22d. 06h. 01m. 31s. 34-6±2 0 km./sec.;
1948 Dec. 22d. 08h. 50m. 15s. 38-7±l-6 km./sec.;
giving a weighted mean of 37-4±l-3 km./sec. No further success was
achieved in 1949 or 1950, but in 1951 a larger scale effort was made using
two equipments simultaneously. Over the period of the Ursid stream
thirty-six velocities were measured with a distribution shown in the
histogram of Fig. 159. The wide spread in this distribution indicates well
the difficulties of measurement where the hourly rate is only a little in
excess of the sporadic background rate. It was unfortunate that on this
occasion the maximum hourly rate of the Ursid stream was only thirteen,
which is considerably lower than in the previous years.
(e) Orbit
So far the velocity measurements are not precise enough to justify any
orbital calculations other than on the assumption that the meteors are
moving with the parabolic velocity. The appropriate orbital elements
for this case have been calculated by Ceplecha,! for the Skalnat6 Pleso
f Clegg, J. A., Lovell, A. C. B., and Prentice, J. P. M. (1949), loc. cit.
x Ceplecha, Z. (1961), loc. cit.
324 THE MAJOR METEOR SHOWERS—III XV. §4
observations, and by Hawkins and Miss Almondf for the British visual
and radio-echo observations. The elements are compared with those
for Periodic Comet Tuttle 1939 k in Table 124.
Table 124
Orbital Elements for the Ursid Meteor Stream and for Comet Tuttle
1939 k
Date
1946
1947
1948
1949
Periodio
Comet
Tuttle
1939 k
Source
Ceplecha
Hawkins and Miss Almond
Mean of radio-
echo and visual
Radio-echo
Radio-echo
2171°
199-3±8
206-8± 10
207-1 ±8
• •
Radiant L
+ 76-81°
+ 76-5±5
+ 82-8±8
77-6±3
• •
SI •
270 66° ±05
2705
269-4
270-2
269-8
Aft Shower
..
• •
- 1-0
-0-6
• •
limits
• •
• •
+ 1-2
+ 11
• •
*
CO • • •
205-85° ±03
213±4
212±5
210±3
207
i
53-57°±-08
57 ±6
60 ±9
56 ±3
65
q (a.u.)
0-93887 ± 0-00011
0-91 ±-02
0 91 ±02
0-92±-01
1-02
Fio. 160. The mean orbit of the December Ureids as plotted from the data of
1946-9, compared with the orbit of Comet Tuttle 1939 k. The orbit of the
comet has been drawn in the plane of the paper, and the orbits of the earth and
the meteor streams have been projected on to it.
All radiant positions have been corrected for zenithal attraction and
diurnal aberration, and reduced to the common equinox of 1950.
f Hawkins, G. S., and Almond, M. (1960), loc. cit.
326
XV, §4
v |4 PERMANENT STREAMS OF SEPT. TO DEC.
SSSSSS^S
t Hawkins. G. S.. and Almond, M. (1950), loc. cit.
XVI
THE MAJOR METEOR SHOWERS—IV
THE PERIODIC STREAMS
The previous three chapters have described the major night-time
meteor showers which recur annually with appreciable intensity, and
from which the debris must be fairly uniformly distributed around the
orbit. At least three remarkable cases are known, however, in which
great showers occur periodically and in which the debris must still be
localized in a small section of the orbit. Two of these, which are still
active—the Giacobinids and Leonids—are described in this chapter.
The third—the Bielids—was last observed in 1899, and has since
disappeared. It is therefore classed under the lost streams of Chapter
XVH. It is also possible that periodic streams may exist amongst the
sequence of day-time meteor showers described in Chapter XVIII, but
sufficient time has not yet elapsed for the existence of such periodicities
to be manifest.
1. The Giacobinid shower
(a) History
By far the most spectacular meteor displays of the present century
have been given by the Giacobinid, or Draconid, meteor shower. The
last intense shower seen visually was in 1946 October, but in 1962 October
an appreciable shower was recorded by radio-echo apparatus during the
day-time. The possibility that the debris of the Comet 1900 (III) dis¬
covered by Giacobini in December 1900f might give rise to a meteor
shower seems to have been first suggested by Davidson X in 1915. David¬
son investigated the list of comets observed since 1892 and selected those
with elliptical orbits. Of these he found only two which passed close to
the earth’s orbit, one of which, Comet 1900 (III), had aperiodic time of
6-6 years. Davidson concluded that, if the debris was spread across the
orbit for some 2,000,000 miles, a shower might be expected at the
descending node around October 10 with a radiant at a 267°, 8 +60°, and
that the relative velocity of the meteors should be about 22 km./sec. He
referred to a feeble shower observed by Denning between October 4
and 17 at a 270°, 8 -f 46°. Denning§ also mentioned the topic in 1918,
t The comet was found again by Z inner in 1913 November, and is now generally
referred to as the Giacobini-Zinner Comet.
X Davidson, M., J. Brit. Astr. Assoc. 25 (1916), 292.
§ Denning, W. F., J. Brit. Astr. Assoc. 28 (1918), 229.
327
XVI §1 THE PERIODIC STREAMS
-a -.« *“ * 71 “™-
observed on 1914 September 23, 24, at a 270 , 8 +50 g
related display. , . r ormer calculations
In 1920 Davidsont published correcUon. to h.s » ^ ^ ^
which arose because the value of o> for position of the radiant
to the elements of the comet given for radiant should be
r r r - -
« d tta Bhowers then «itnw*d .» cW MV t to f
meteoric storms which have occurred during the past century. &
Z sZ investigated the ancient records of
rallvsis of the relative position of the earth and the comet at the
. tot -turn, of a.
have been witnessed in a.d. 585, 859, 1385, 1841, and 1847.
(6 The otcobinid shower has now been observed on four "1926
1933, 1946, and 1952. In 1926, the earth crossed the cometary orb
days before the comet; in 1933, 80 days after the comet and, ml1946
days after the comet. In 1939 the orbit was crossed 136 days before th
comet and no shower was observed, but m 1952, when the orbit was
crossed 195 days ahead of the comet, an intense shower was recorded
daylight by the radio-echo apparatus.
The 1926 observations have been described by Prentice|| and y
Denning.tt Prentice observed in a clear sky for 3 hours between 20h.
20m. and 23h. 20m. on October 9 and estimated the hourly rate from the
radiant in Draco to be about seventeen. By far the most specUcular
event of this return was, however, the occurrence of a grcat fireball on
1926 October 9d. 22h. 16m. U.T. from the Draco radiant. Thirty-five
t Davidson, M„ Mon. No,. Roy. Astr. Soc-80 (1920), 739.
t This information is given by Dennmg W. F., ibid. 87 (19-6).
§ Fisher, W. J., Bull. Uorv. Coll. Ob,. 0934),.no. 894. 15.
|| Prentice, J. P. M.. J- Bn,. As,r. Assoc. 44
tt Denning, W. F., Mon. Not. Roy. Astr. Soc. 87 (1926), 104.
104.
328
THE MAJOR METEOR SHOWERS—IV
XVI, §]
observations were found to be suitable for analysis. The original data
were computed by Kingf and a full description of the observations was
published later by Porter and Prentice. J This fireball was of zenithal
magnitude —7 and left a long-enduring train which persisted for between
32 and 40 minutes.
Records of the watches in the intervening years 1927-32 inclusive
have been given by Prentice§ and show no activity from the shower. On
1933 October 9, however, when the earth crossed the orbit 80 days behind
the comet, a great meteoric storm was witnessed in many parts of the
world. Most of the observers in England§ were handicapped by cloud
but King|| has collected and summarized many reports from other parts
of the British Isles and from observers widely scattered in Europe. It
is evident from these reports that the total duration of the shower was
only some 4 to 4-5 hours and that the maximum occurred at 20h. on
1933 October 9. The numbers were so great that few observers were
able to count the rate, but it seems clear that the rate at maximum must
have been 4,000 to 6,000 per hour. The most detailed information is
that obtained by de Royft in Belgium and by Sandig and Richter# in
Leipzig, who undertook telescopic observations. A comparison of these
visual and telescopic data has been made by Watson.§§ The hourly-rate
curve obtained by de Roy (Fig. 161), shows a sharp maximum of about
6,400 per hour at 20h. 15m. U.T. He also made magnitude estimates of
534 meteors over two periods shown as I and II in Fig. 161. These
observations confirm the statement of nearly all observers that the
majority of the meteors were faint. The analysis of this magnitude
distribution and of the telescopic magnitude distribution will be dis¬
cussed in Chapter XIX. Emanuelli|||| made a critical analysis of a great
number of observations which were published on the 1933 shower, from
which he concluded that the maximum was at 20h. 4m., when the
hourly rate was 19,000.
Attempts to observe the shower in England at the 1939 and 1940
return have been described by Prentice.ttt No Giacobinid meteors were
found but in view of the short period characteristics of the shower in
t See Denning, VV. F. (1926), loc. cit., and Prentice (1934), loc. cit.
x Porter, J. G., and Prentice, J. P. M., J. Brit. Astr. Assoc. 49 (1939), 337.
§ Prentice, J. P. M., J. Brit. Astr. Assoc. 44 (1934), 110.
|| King, A., ibid., p. 111.
ft de Roy, F., Gazette Astronomiquc, 20 (1933), 170.
Xt Sandig, H., and Richter, N., Astr. Nachr. 250 (1933), 170.
§§ Watson, F., Bull. Harv. Coll. Obs. (1934), no. 895, 9.
1111 Emanuelli, P., Coelum, 9 (1939), 161.
ftt Prentice, J. P. M., J. Brit. Astr. Assoc. 50 (1939), 27; 51 (1940), 18.
329
XVI> §1 THE PERIODIC STREAMS
1933 and 1946 it appears that daylight may have interfered with the
observations, since the predicted time of maximum fell after dawn m
1939 and during the afternoon in 1940-t However, there are no reports
of any appreciable shower from other parts of the world.
Fio. 161. The activity of tho Giacobinid shower on 1933 Oct. 9
according to the visual observations of do Roy. I and II represent
tho times when magnitudo estimates were made of 534 moteors.
The return of the shower in 1946 was well observed visually, photo¬
graphically, and by the new radio-echo technique in many parts of the
world. The shower was again a spectacular occurrence, of short duration
—not more than 5 to 6 hours—and with a sharp peak at 1946 October
lOd. 3h. 40m. to 3h. 50m.
The activity as found by the various techniques is illustrated in the
composite diagram of Fig. 162. The visual records are those compiled
by WylieJ from six observing groups in America, the photographic
records are those given by Jacchia, Kopal, and Millman§ from the
Canadian observations and the radio-echo records are from the results
obtained in England by Lovell, Banwell, and Clegg|| at Jodrell Bank.
Very similar radio-echo results were also obtained by Appleton and
Naismithtt at Slough and by Hey, Parsons, and Stewart JJ at Byfleet.
It is evident from these observations that the characteristics of the
f Tho experience of 1952 when a shower was observod by the radio-echo technique
in day-time, with the comet even farther from perihelion, supports the suggestion that
the shower may have been missed in 1939 and 1940 because of daylight.
x Wylie, C. C., Sky and Telescope, 6 (1947), no. 66, 11.
§ Jacchia, L. G., Kopal, Z., and Millman, P. M., Astrophys. J. Ill (1950), 104.
|| Lovell, A. C. B., Banwell, C. J., and Clegg, J. A., Mon. Not. Roy. Astr. Soc. 107
(1947), 164. ft Appleton, E. V., and Naisraith, R., Proc. Phys. Soc. 59 (1947), 461.
XX Hoy, J. S-, Parsons, S. J., and Stewart, G. S., Mon. Not. Roy. Astr. Soc. 107 (1947),
176.
330
THE MAJOR METEOR SHOWERS—IV
XVI, § 1
shower were very simil ar to those of the 1933 return. The hourly rate at
maximum according to the visual plots of Wylie was 4,200. According
Fio. 162. The activity of tho Giacobinid meteor shower on 1946 Oct. 10.
(o) Visual, (6) photographic, (c) radio echo.
to the cin6-film analysis of the radio-echo results of Lovell, Banwell, and
Clegg, 67 echoes were recorded in 24 seconds at the peak, giving an
equivalent hourly rate of 10,000; but within ±5 minutes of this peak the
hourly rate had decreased to 3,000 and within ±30 minutes to 60. The
sensitivity of this apparatus was such as to give a close relation to the
hourly rates seen by a single visual observer.
331
XVI 51 THE PERIODIC STREAMS
Prenticef has summarized the results of the British visual ob 86 *^***™^
Averagtag over 7- or 8-minute intervals yielded a —-n observed
rate of 965 which, when allowance was made for the bw altitude of t
radiant, gave an equivalent zenithal rate of 2,250. Also, using de Roy s
magnitude distribution for the 1933 shower, Prentice makes an allow¬
ance for the strong moonlight and concludes that the 1946 ">turn was
only half as rich as that of 1933. This conclusion is not bo ™ e ° ut by th ®
visual results of Wylie or by the radio-echo observations, both of which
indicate that the shower was at least as intense as the 1933 return.
An interesting feature of the activity shown in Fig. 162 is the sudden
temporary decrease at about 3h. 30m„ evident in the ^sual photo
craphic and JodreU Bank radio records. Jacchia, Kopal, and MillmanJ
remark that a similar drop is also evident in the final frequency curve
compiled from all the Canadian visual observations.
It is also seen that the radio-echo rates appear to have reached a
maximum a few minutes before the visual and photographic maxima,
but a subsidiary maximum occurred at the time of the visual and
photographic maxima. Experience on other showers, and with the
sporadic background, showed that the hourly rates given by the radio
apparatus and a visual observer were very similar. Although the radio
apparatus samples fainter meteors, its restricted collecting area balances
the difference. It may be, therefore, that this high peak at 3h. 40m.
consisted of meteors too faint to be visible, and that a separation of meteor
masses has already taken place in the Giacobinid stream. It will bo
noticed that the subsidiary maximum at 3h. 48m. agrees well in time and
hourly rate with the visible maximum.
Subsequent radio-echo surveys in 1947-51 showed no unusual activity
at the time of the passage of the earth through the orbit of the comet.
On 1952 October 9, however, the radio-echo apparatus recorded an
intense shower during daylight hours in the afternoon.§ The shower
commenced at 14h. 30m. U.T. and rose rapidly after 15h. to a maximum
at 15h. 30m. After this time the shower declined quickly, and by 16h.30m.
the activity had fallen to a small fraction of the maximum. The equi¬
valent visual hourly rate during the period of maximum was estimated
at 200. One or two meteors at the end of the shower in the early evening
were observed visually.§ The summarized data on the activity of the
shower are given in Table 125.
f Prentice, J. P. M., Observatory, 67 (1947), 3; J. Brit. A sir. Assoc. 57 (1947), 86.
x Jacchia, L. G., Kopal, Z., and Millraan, P. M. (1950), loc. cit.
§ Brit. Astr. Assoc. Circ. (1952), no. 337.
THE MAJOR METEOR SHOWERS—IV
XVI, § 1
332
Table 125
Activity of the Giacobinid Shower
Date
Earth at node
Hourly rate at maximum
1926
70 days before comet
17
1933
80 days after comet
4,000-6.000
1939
136 days before comet
• •
1946
15 days after comet
4,000-6,000
1952
195 days before comet
200
(c) Radiant
From the observation of fourteen meteors during the first appreciable
shower in 1926, Prenticef gave the mean corrected radiant as a 260°,
8 4-51*5°, with a radiant diameter of 7°. The computation of the radiant
of the great fireball was made by KingJ from thirty-five observations
and is given as a 262°, 8 4-55°. The very close agreement of these
positions with the predicted radiant position (see (a)) left little doubt
of the association of the shower with the comet.
During the great shower of 1933 many radiant positions were com¬
puted, a large number of which have been collected by King.§ Represen¬
tative determinations are listed in Table 126.
Table 126
Visual Determinations of the Giacobinid Radiant during the
1933 Return
Observer
Number of meteors
used in determining
the radiant
Radiant position
a 8
Diameter
deg.
deg.
deg.
Ellison, Armagh
• •
267
+ 65
3
Milligan, Omagh
> •
264-6
54-5
• •
Dods, Eskdalemuir .
• •
265-25
52-3
• •
Walmesley, Perth
. ■
265
55
• •
Mourant, Jersey
. •
256-5
54
• •
de Roy, Antwerp
16
262
55
7
Ryvos, Spain .
• •
266
63-6
••
Forbes-Bentley, Malta
• •
262-5
65
• •
Sytinskaja, Leningrad
110
267-2
55-9
(Corrected a 262-1
8 +65-8)
Astapowitech, Stalinabad .
80
258-0
67-5
• •
Malzman, Odessa
18
267
57
• •
Schwarzman, Odessa
15
265
15
• •
(263
47 \
Results of 25 observers on
Limits
1 10
to j
• •
the Continent
1282
60 J
t Prentice. J. P. M. (1934), loc. cit.
X Quoted by Donning, W. F. (1926), loc. cit., and by Porter, J. G., and Prentice,
J. P. M. (1939), loc. cit.
§ King, A. (1934), loc. cit.
033
XVI §1 THE PERIODIC STREAMS
Accurate photographic determinations of the radiant position were
made by Jacchia, Kopal, and Millmanf during the 1946 » ho ™. ™J
used three cameras, behind one rotating shutter, mounted so as to cover
4 000 square degrees of the sky. Over the periodof the Giacobimd shower
sixteen exposures were made on each camera, the average exposure time
being 15 minutes. By this means they obtained photographic information
of 204 Giacobinid meteors, each plate containing the photographed trails
of a number of meteors. The cameras were stationary; hence the
individual radiant points of all the meteor trails on one exposure defined
a curve on the film, resulting from the composition of the proper motion
of the radiant and the diurnal motion of the sky. The proper motion
was computed on the assumption that the meteor particles followed the
orbit of the Giacobinid comet exactly and this was combined with the
diurnal motion to give the apparent path of the radiant on the films.
A visual watch was carried out simultaneously with the photographic
recording and 27 meteors visually observed were identified with 27 of
the photographed meteors. The time of apparition of these 27 meteors
was therefore known accurately. In Table 127, which gives the results
of the computation of the radiants, these 27 visually identified meteors
are included separately in 6 groups.
Table 127
Photographic Determination of the Giacobinid Radiant during the
1946 Return
Exposure set
or visual
meteor group
Mean time
1946 Oct. 10
Number oj
meteors in
group
Apparent radiant
(1947-0)
a 5
True radiant cor¬
rected for diurnal
aberration and
zenithal attraction
(1947-0)
a 8
731-732
1-501
7
deg.
266 500
deg.
55 048
deg.
261-765
deg.
54-039
735
2-583
19
267-235
55-822
261-988
54-143
1
2-667
7
266959
55-782
261-692
64-027
736
2-833
9
267-257
56 057
261-923
54-205
2
2-943
3
267-432
56 125
262-078
54-210
737
3-117
10
267-422
56-177
262 033
54-124
3
3-202
5
267 495
56-223
262-092
54-110
738
3-307
29
267-732
56-261
262-317
54-081
4
3-460
4
267 580
56-405
262-141
54-121
739
28
267-519
56-463
262-075
54-051
5
3-763
4
267-312
56 618
261-859
64-071
740
42
267-511
56 692
262 056
54 130
741
267-324
56-773
261-898
54-004
6
4-750
4
267-403
57-357
262-136
54-048
f Jacchia, L. G., Kopal, Z., and Millman, P. M. (1950), loc. cit.
334
XVI, §1
THE MAJOR METEOR SHOWERS—IV
A least squares solution for the true radiant gave
1946 Oct. 1016 /“- 262 -°
\8 = +64-
= 262-07°±0 13 (1947 0)
= +54 09°±0 04
with a daily motion of (+2-l°±0-9
The motion of the true radiant is direct at a rate of l-3°±0-6 per day,
but the authors point out that the reality of this is in doubt because of
the relatively large probable error.
For the twenty-seven trails which were also visually observed it was
possible to determine the distance of the projected trails from the mean
computed radiant. The average value was 7-2', giving a probable error
of spread of 6*2'. The authors conclude that most of this spread can be
accounted for by observational errors and that the true cosmic spread
was probably less than 2 or 3 minutes of arc. This is very much smaller
than the cosmic spread of many other of the major showers (for example,
Taurids 17' Geminids 13*6'; see Chap. XV). This small spread is
in marked contrast to the large radiant diameter found in the visual
observations.
(d) Velocities
Until the 1946 return there were no well-attested measurements of
the velocities of the Giacobinid meteors. Most of the visual observers
had remarked that the meteors were slow in accordance with the
original predictions made by Davidson,f and the velocity of the 1933
fireball was computed by KingJ from thirty-five observations to be
32 km./sec. The meteors were so clearly moving in the orbit of the comet,
however, that little doubt existed as to their velocity. Computation of
the relative velocity of the earth and the meteors was made by Jacchia,
Kopal, and Millman§ using Cunningham’s|| orbit for the comet. They
obtained the value of 20-433 km./sec. before correction for zenith
attraction. The computed geocentric velocity corrected for diurnal
aberration and zenith attraction is given in Table 128 for the duration
of the shower. The authors expressed confidence that these velocities
were correct to 1 in 1,000, since the observed position of the radiant on
October 10-16 differed by only 4-5' from its computed position, this
divergence being less than the probable error.
| Davidson, M. (1916), loc. cit.
x Seo Porter, J. G., and Prentice, J. P. M. (1939), loc. cit.
§ Jacchia, L. G., Kopal, Z., and Millman, P. M. (1960), loo. cit.
|| Cunningham, L. E., Harvard Announcement Card, no. 776.
THE PERIODIC STREAMS
Table 128
Computed Velocities of the Giacobinid Meteors 1946
The only velocity measurements actually made during the 1946 shower
appear to be the radio-echo measurements of Hey, Parsons, and Stewart. |
These were remarkable as being the first velocity measurements ever
made by radio-echo methods. The technique, in which the reflection from
the head of the approaching meteor is observed, has been desenbed in
Chapter IV. Twenty-two measurements were made, giving the data
listed in Table 129.
Table 129
Radio-echo Measurements o} the Giacobinid Velocities 1946
The weighted mean of the velocities, 22-9±l-3 km./sec., uncorrected
for zenith attraction or diurnal aberration, has to be compared with the
computed value, quoted above, of 20-433 km./sec.
(e) Orbit
The observations described above confirm Davidson’s original predic¬
tion that the debris asso dated with the Giacobini-Zinner Comet is respon¬
sible for the meteor showers observed in 1926, 1933, 1946, and 1952.
As far as the meteor showers are concerned, chief interest, therefore,
| Hey, J. S., Parsons, S. J., and Stewart, G. S. (1947), loc. cit.
Table 130
Changes in the Orbit of Comet Giacobini-Zinner since 1900
336
THE MAJOR METEOR SHOWERS—IV
XVI, § 1
XVI. § I
337
THE PERIODIC STREAMS
centres on the effect of perturbations, especiaUy in regard to possible
future close encounters of the earth and the comet. The relation be¬
tween these approaches and the intensity of the meteor shower has been
given in Table 125. Future returns of the comet will be awaited with
great interest. The 1946 elements of the comet and the predicted
elements for the subsequent return in 1953, after allowing for the per¬
turbations by Earth, Jupiter, and Saturn, are given in Table 131.
2. The Leonid shower
(a) History
The history of the remarkable Leonid shower has been related by
Olivier.f The spectacular events during the night of 1833 November 12,
when meteors wore described as ‘falling from the sky like snowflakes ,
represents, perhaps more than any other event, the beginning of scientific
interest in meteor astronomy. Likewise, the failure of the shower to
return as predicted in 1899 represents in the opinion of Olivier ‘the
worst blow ever suffered by astronomy in the eyes of the public’. The
display of 1833 drew attention to the accounts of a similar spectacle
observed during the night of 1799 November 11. The well-known
account by Humboldt, who observed this event in South America,
referred to ‘thousands of meteors and fireballs moving regularly from
north to south with no part of the sky so large as twice the moon’s
diameter not filled each instant by meteors’. It was during the 1833
display, however, that serious scientific observations were first made,
particularly by D. Olmsted, A. C. Twining, and many others who noticed
that the meteors appeared to be radiating from a point. In 1863 and
1864 NewtonJ predicted the dates on which previous occurrences of the
Leonid shower should have been witnessed and succeeded in tracing its
occurrence back to a.d. 585, and also predicted that the shower would
return again in November 1866. In 1866 Schiaparelli’s orbit for the
Leonids was published in his Sternschnuppen and the close connexion of
this orbit with that of the newly discovered Comet 1866 I was immedi¬
ately realized. A period of 33-25 years was assigned to the shower, and
the expected appearance of another great display on 1866 November 13
was confirmed, although the rate does not appear to have been as great
as that in 1833. In the years following this shower J. C. Adams and
Stoney investigated the Leonid orbit and the possibility of perturbations
in detail. In spite of the caution advanced by such calculations—in
f Olivier. C. P., Meteors, ch. 4.
t Newton, H. A., Sillimans Journal (II), 36 (1863), 146; 37 (1863), 377; 38 (1864), 53.
3605.66
Z
338 THE MAJOR METEOR SHOWERS—IV XVI, § 2
particular that on the critical date in November 1899 the earth would
be 1,300,000 miles from the Leonid orbit—another great shower was
confidently expected in November 1899.f
The failure of the shower to manifest itself undoubtedly led to a serious
diminution of interest in meteor astronomy. At the next perihelion
passage in 1932, although a major shower occurred, there was no great
meteoric storm such as had been witnessed a hundred years earlier. It
now seems certain that the main part of the Leonid orbit has been
removed from the earth’s orbit by successive perturbations, and the
recurrence of the tremendous meteoric storms of the Leonids in the
future seems unlikely.
(6) Activity
The period of the Leonid stream is 33*25 years and the debris still seems
to be closely grouped around the comet. Even during the epoch of the
great meteoric storms, appreciable activity only seems to have been re¬
corded for a few years either side of the maximum, the shower otherwise
appearing with low intensity. Some of the available data on the activity
around the appropriate times of perihelion passage are given in Table 132.
The hourly rates quoted are the maximum observed in any part of the
world. As will be mentioned later, the shower is of short duration and in
several cases observers in England, for example, have recorded only
comparatively low rates because the maximum has occurred in day¬
light, whereas in some parts of America the full maximum has been visible.
f The following account, given by the Director of the Meteor Section of the British
Astronomical Association (W. F. Denning), reveals the high state of oxpectancy which
prevailed—Afem. Brit. Astr. Assoc. 9 (pt. i) (1900), 6: ‘Another failure! Yet it was
thought that tho display of 1899 would more than compensate for the weak showers of
1897 and 1898. The failure is much deplored in view of the universal effort to witness
the phenomenon and secure useful observations. No meteoric event ever before aroused
such an intense and widespread interest, or so grievously disappointed anticipation.
The scientific journals and newspapers all contained references to the subject, and the
occurrence was predicted in such confident terms to take place that the public became
enthusiastic, and looked forward to its appearance as a certainty. Many people regard
the prescience of the astronomer as something marvellous, he can foretell the moment
of an eclipse that will occur generations hence, and no thought of questioning either his
accuracy or veracity ever enters their heads. Thus everyone expected that when they
looked up to the sky on the night of November 14-15 they would see it full of meteors.
But the fiery storm did not appear. The firmament, with its glittering stars and silver
moon, was just as still as on an ordinary mid-November night. Only now and then,
indeed, a shooting star rapidly streaked along the sky to prove that the Leonids wore
present in a weak and scattered shower in place of the dense and brilliant display that
had been awaited. The finest celestial sight of a generation had failed to come at its
appointed time, and the disappointment was all the keener in some quarters from the
impression which prevailed that another chance of witnessing it would not occur until
1933.’
XVI, §2
THE PERIODIC STREAMS
339
Table 132
Activity of the Leonid Shower
Date
Hourly rate
Source
1799 Nov. 11
Great storm
Humboldt
1831 Nov. 13
? Considerable shower "l
1832 Nov. 12-13
T \
soe Olivierf
1833 Nov. 12
Great storm (10,000 ?)J
1866 Nov. 13
5,000 I
1867 Nov. 13
1 , 000 +(moon) S
6eo Olivierf
1868 Nov. 13
1,000 J
1897 Nov.
Very low
1898 Nov. 14
50-100
1899 Nov. 14
40
1900 Nov.
Very low
British
1901 Nov. 14
200 +
Astronomical
1902 Nov.
Very low
Associationf
1903 Nov. 15-16
250§
1904 Nov. 14
20-50
1906 Nov. 16
20-3011
1930 Nov. 16
30-80 1
British
1931 Nov. 16
30-90 >
Astronomical
1932 Nov. 10-17
240 (see Crommolintt) J
Association f
1946 Nov. 17
24 1
1947 Nov. 16
3
1948 Nov. 14
11
1949 Nov. 16
7
Radio-echo ratoaj
1950 Nov. 16
11
1951 Nov. 17
< 8
1952 Nov.
No record
1953 Nov. 17
< 7
During the period for which systematic observations have been
possible using the radio-echo techniques, no major return of the shower
has taken place. The radio-echo rates for the years 1946-53 are in¬
cluded in Table 132.
The association of close grouping of the debris near the comet with a
small cross-section is again in evidence in the case of the Leonids. All
reports of the great meteoric storms refer to the short duration of the
shower. For example, in England during the 1866 return the maximum
occurred at about Olh. on November 13 and the shower was over by 04h.
Denning§ has given the hourly-rate curve for the unexpectedly rich
return of 1903 as shown in Fig. 163. The extreme sharpness of the
maximum bears a strong resemblance to the sharp curve of activity
t Olivier, C. P., Meteors (1925), ch. 4.
X Mem. Brit. Astr. Assoc. 6 (1897) et soq.
§ Denning, W. F., Mon. Not. Roy. Astr. Soc. 64 (1903), 125.
|| See ibid. 67 (1907), 275. tt J- Brit. Astr. Assoc. 43 (1933), 99.
ft Hawkins, G. S., and Almond, M., Mon. Not. Roy. Astr. Soc. 112 (1952), 219, and
unpublished Jodrell Bank data.
Ltm&txuU of Slot WSO-O)
a * i7 * n 20
NevOKber
Fio. 164. Frequency of Leonid meteors per 100 hours exposure
on the Harvard photographic plates 1898-1951.
Harvard from 1898 to 1951.f The frequency per 100 hours exposure is
shown in Fig. 164. One-half of the photographic meteors appeared within
a 24-hour interval around the maximum.
(c) Radiant
The great shower in November 1833 was the first occasion on which it
became evident that the meteors were apparently radiating from a point.
t Wright, F. W., Tech. Rep. Harv. Coll. 06s. (1951), no. 7 (Harvard Reprint Series, H-38).
341
XVI | 2 THE PERIODIC STREAMS
The credit for this observation is generally given to D. Olmsted and
A. C. Twining, but according to Olivierf the facts were also clearly
stated by several other observers. The scientific preparations for the
expected return in 1899 were so extensive that although the storm did
not then materialize a large number of radiant positions were determined
in the subsequent years, both by photography and by visual observation
Denning! gave the radiant as a 150-65°, 8 -f23-l° for the mean o
seventeen doubly observed Leonids in the years 1896-1903. This showed
good agreement with the more extensive determinations§ made in 1903,
a sample of which is as follows:
Blum (Paris) a 151-6° 5 +22-5° (48 meteors)
Denning (Bristol) <* 151° 5+22° (33 meteors)
Olivier (Virginia) a 151° S+22° (78 meteors)
In 1932 King|| presented an analysis of his own observations of the
Leonids in the years 1899-1904 and 1920-31 with particular reference to
the motion of the radiant. These observations are quoted in Table 133.
Table 133
Visual Observations of the Leonid Radiant according to King ||
Date Q.M.A.T.
Sun's longitude
a
5
No. oj meteors
Radiant
diameter
1899 Nov. 15-62
© deg.
144-3
deg.
151-5
deg.
+ 22
7
deg.
4
1900 Nov. 16-61
144-0
151-5
22
3
3
1903 Nov. 15-86
143-5
150
22-5
10
• •
1904 Nov. 15-61
144-0
150-5
21
8
• •
1920 Nov. 13-97
142-5
150
22-5
7
• •
1920 Nov. 15-66
144-1
152
23
7
4 3
1925 Nov. 15-54
143-9
150-5
23
3
• •
1927 Nov. 17-56
1454
152
22-5
4
0-5
1928 Nov. 15-59
144-2
150-25
22
10
1-75
1928 Nov. 16-60
145 2
151-75
22
6
2
1930 Nov. 15-58
143-7
151
22
6
3
1930 Nov. 16 67
144-7
152
21-5
8
1-75
1931 Nov. 16-60
144-5
152
22-2
22
1-66
1931 Nov. 17-58
145-5
153
22
8
4
After adjusting the dates for epoch and correcting for precession to 1932,
King gave the weighted means listed in Table 134.
f Olivier, C. P., Meteors (1925), ch. 4.
J Pa nnin g, YV. F., Mon. Not. Roy. Aslr. Soc. 64 (1903), 125.
§ Denning, YV. F., ibid. 64 (1904), 354.
|| King, A., ibid. 93 (1932), 109.
342
XVI, §2
THE MAJOR METEOR SHOWERS—IV
Table 134
Change of Mean Radiant Position of Leonids with Date according
to King
Dale
1932 O.M.A.T.
O deg.
Mean position
No. of radiants
Nov. 13-97
142-5
a (deg.)
150-2
5 (deg.)
+ 22-4
1
Nov. 15-42
144-0
151-0
22-2
7
Nov. 16 09
144-7
152-0
21-9
4
Nov. 16-82
145-4
152-5
22-2
2
This appears to be the first collected observational evidence of the shift
of the radiant. King’s predicted ephemeris for the radiant based on this
shift is given in Table 135.
Table 135
King's predicted Ephemeris of the Leonid Radiant
Date
1932 O.M.A.T.
Radiant
Date
1932 O.M.A.T.
Radiant
Nov. 12-5
a (deg.) 5 (deg.)
148 3 +23-2
Nov. 16-5
a (deg.) 5 (deg.)
152-3 -4-21-8
Nov. 13-5
149 3
22-8
Nov. 17-5
1533
21-4
Nov. 14 5
150-3
22-5
Nov. 18-5
154-3
21-0
Nov. 15-5
151-3
22-1
• •
King’8 ephemeris is in close agreement with the mean radiants given
by Huruhataf from an analysis of the visual Japanese observations
made in 1934, listed in Table 136.
Table 136
The Visual Leonid Radiant 1934 according to Huruhataf
Date
1934 O.M.A.T.
Radiant
a
5
deg.
deg.
Nov. 3-8
141
+ 27
Nov. 7-8
145
25-5
Nov. 9-8
146
25
Nov. 10-8
147
24-5
Nov. 14-8
151
22-5
Nov. 15-8
151-8
22-2
Nov. 16-8
152-7
21-8
Nov. 17-8
153-3
21-5
t Huruhata, M., Mem. Jap. Astr. Assoc. 3 (1935), 327.
343
XVI( §2 THE PERIODIC STREAMS
Photographic determinations of the Leonid radiant were first made
in 1898 at Yale and Harvard. The Yale results have been ^cuwed by
Elkin.f The mean radiant determined from seven trails was at a 15 ,
S +22-6°, with a spread of about half a degree in each coordinate. At t
same time a considerable number of trails were also photographed a
Harvard. A discussion of three trails which appeared on one plate on
1898 November 14 has been given by Hogg.J The mean posiUon w«-at
R A 10h 03m. Is., 8 +22-36° (1900), but the trails did not intersect in a
point, the spread lying between 12 -5 and 3S'-6. from which Hogg con-
eluded that the luminous air paths could not be exactly parallel. The
analysis of the further fifteen trails obtained with the guided cameras ■on
1898 November 14 has been given by Fisher and Miss Olmsted.§ The
weighted mean position of the radiant was found to bo a 151 00-5 ,
S +22° 381'. Fisher and Miss 01msted|| also give the results of the
analysis of three Leonid trails on a single plate exposed on 1901
November 14. The weighted mean radiant was at a 150 49-7 ,
8 +23° 27-3', the triangle of intersection of the three trails extending
The latest analysis of the Harvard photographic Leonid data has been
given by Miss Wright, ft The analysis included thirty trails photographed
at one station and six doubly photographed trails in the period 1898 to
1951. The trails previously analysed by Fisher and Miss Olmsted are in¬
cluded in the series. The results of this analysis are given in Table 137,
which gives the data for the corrected Leonid radiant at maximum, in
Table 138, which gives the predicted position of the corrected radiant
from November 15 to November 20, and in Fig. 165, which gives the path
of the mean radiant and the positions of the individual determinations.
Table 137
Corrected Leonid Radiant at Maximum from the Harvard
Photographic Data
Mean long, of sun at max. 233°-94 1
Right ascension a at max. 152° 17' V Equinox 1950 0
Declination 8 at max. +22° 17'
AacosS (per day) +39'±3'
AS (per day) — 25'±3'
Total daily motion 46'
t Elkin, W. L., Aslrophys. J. 10 (1899), 25.
t Hogg, F. S., Bull. Harv. Coll. Obs. (1928), no. 857, 6.
§ Fisher, W. J., and Olmsted, M., ibid. (1929), no. 870, 7.
II Fisher, W. J., and Olmsted, M., ibid., p. 12. . .
ft Wright, F. W., Tech. Rep. Harv. Coll. Obs. (1951), no. 7 (Harvard Reprint Senes,
11-38).
344
XVI, §2
THE MAJOR METEOR SHOWERS—IV
Table 138
Predicted Mean Radiant Position (1950 0) from the Harvard
Photographic Data
Date U.T. Nov.
O {deg.)\
a {deg.)
5 {deg.)
15
232-5
151°17'
+ 22° 53'
16
233-5
151 69
22 28
17
234-5
152 41
22 03
18
235-5
153 23
21 38
19
236-5
154 06
21 14
20
237-5
164 48
20 49
The agreement between the visual and photographic radiant deter¬
minations is extremely good.
(d) Velocities
Aa soon as the well-marked period of 33-25 years for the recurrence
of the Leonid stream had been established, the velocity of the meteors
could be computed accurately. The geocentric velocity outside the
atmosphere should be 72 km./sec. The discrepancy between this value
and the earlier measurements of the velocity of the Leonid meteors was
put forward as strong evidence for considerable deceleration in the
atmosphere. Thus, in the early photographic work described in Chapter
XI, Millman and Miss Hoffleitf measured the velocity of three Leonids as
61-3, 78, and 61-1 km./sec. and derived a mean heliocentric velocity of
31 km./sec. instead of the expected value of 41 -5 km./sec. In his analysis
of the British visual meteor data, Porter}: found the mean of twenty-
seven Leonid determinations to be 67-8 km./sec. It now seems evident,
however, that these low values must be due to errors of measurement’,
since the contemporary measurements using the double-station photo¬
graphic technique give results in close agreement with the expected
velocity and show only small decelerations. Six double-station measure¬
ments have been published by Miss Wright,§ according to the analysis
made by Jacchia.|| The results are given in Table 139.
The random errors in measuring the velocities of the Leonid meteors
are considerably larger than for most doubly photographed meteors,
owing to the fact that the trails are short and faint. The average number
of breaks in the trail was only six, resulting in a weak velocity determina-
t Millman, P. M., and Hoffleit, D., Ann. Haro. CM. Obs. 105 (1937), 601.
X Portor, J. G., Mon. Not. Roy. Aetr. Soc. 104 (1944), 257.
§ Wright, F. W. (1951), loc. cit.
|| One of these (No. 792) was published previously by Jacchia, L. G., Tech. Rev. Harv,
Coll. Oba. (1948), no. 2. *
XVI, §2
THE PERIODIC STREAMS
346
JUght Ascension
Flo. 165. Tho path of the mean Leonid radiant as given by the Harvard
photographic results. For each meteor trail of the single-station motcore a
black dot represents the nearest point of the extendod great circle to the
calculated mean radiant of tho instant. The line from each point to tho radiant
is perpendicular to the great circle for each trail. The doublo circles refer
similarly to the meteor trails photographed simultaneously at two stations.
tion and a very poor measure of deceleration. The mean apparent relative
velocity of 71*8 km./sec. must therefore be considered to be in excellent
agreement with the anticipated value from the orbital characteristics of
the parent comet.
(e) Orbit
The first significant speculations on the orbit of the Leonids were made
in 1863 and 1864 by Newton, who fisted five possible periods for the
shower. In 1866 Schiaparelli published an orbit on the assumption that
346
THE MAJOR METEOR SHOWERS—IV
XVI, §2
Table 139
The Velocities of Six Leonid Meteors determined by the
Double-station Technique
MtUor No. (Harvard notation)
792
2176
2179
2181
1360
1447
Da te U.T..
1938 Nov.
1950 Nov.
1950 Nov.
1950 Nov.
1946 Nov.
1946 Nov.
16-374
17-3917
17-4732
18-4796
19-340
20-287
Sun’s longitude O
233®-60
234*-48
234 # -64
235*-65
236°-45
237°-41
Apparent radiant
162* 05'
152* 43'
152* 11'
163* 40'
163* 63'
164* 32'
+ 23° 04'
+21* 26'
+ 22° 59'
+ 21* 32'
+ 21*07'
+ 21* 02'
Corrected radiant
152* 00'
152* 69'
152*09'
163* 32'
.,
154* 43'
+ 22* 65'
+ 21* 21'
+ 22* 68'
+ 21* 30'
..
+ 20* 64'
Apparent relative
velocity v km./sec. .
71-8
72-9
71-9
71-7
71-8
No atmosphere
velocity V km./sec. .
Gcocentrio velocity
72-2
72-9
71-9
72-3
v, km./sec.
Heliocentrio velocity
711
71-8
70-9
■SH
70-8
V km./seo. .
420
426
41-5
41-4
33-25 years was the correct period, and, as mentioned earlier, the identifi¬
cation of this orbit with that of the Comet Temple 1866 I followed
immediately. After this identification Schiaparellif gave the orbits for
the stream compared with that of the comet as listed in Table 140.
Simultaneously, Adams J suggested that the motion of the node should
enable a decision to be reached between the five possible periods suggested
by Newton. The observed motion was 102-6' annually with respect to
the equinox, or 52-6' with respect to the stars, which is 29' in 33-25years.
Adams’s calculation of the perturbations by Jupiter, Saturn, and
Uranus, assuming a period of 33-25 years, gave a motion of 28'. The
excellent agreement finally settled the argument in favour of the largest
of Newton’s five periods. Adams’s elements for the orbit are given in
Table 140. The orbits of five of the Leonids doubly photographed at
Harvard and referred to earlier are also given in Table 140. Miss Wright§
points out that an error of only 0-2 km./sec. in the velocity could account
for the difference of 12 years in the mean period given for the five
meteors and that of the comet.
The task of investigating the perturbations of the orbit in the years
following the 1866 return was carried through by Stoney and Downing.||
They found that the stream made close approaches to Saturn in 1870 and
to Jupiter in 1898, whereby the perihelion distance was decreased from
f Schiaparelli, J. V., SUmscJinupptn (1871), p. 67.
J Adams, J. C., Mon. Not. Roy. Astr. Soc. 27 (1866-7), 247.
§ Wright, F. W. (1961), loc. cit.
|| Stoney, G. H., and Downing, A. M. W., Proc. Roy. Soc. A, 64 (1898-9), 403.
Table 140
xvi. §2
THE PERIODIC STREAMS
348
THE MAJOR METEOR SHOWERS—IV
XVI, §2
0-9855 to 0-9729 and the period changed by one-third of a year. Finally,
just before the expected 1899 return, Stoney showed that on the critical
date Adams’s orbit was 1,300,000 miles inside the earth’s orbit. Unfor¬
tunately, as we have seen, insufficient notice was taken of these cautions
about the improbability of a great return of the Leonids in 1899.
As far as is known, the laborious calculations necessary to establish
the effect of future perturbations on the orbit of the stream have not
been made. From the comparatively weak returns of 1899 and 1932, it is
evident that at the critical date the earth is now far removed from the
dense part of the stream. Whether successive perturbations will increase
or decrease the distance between the earth and the main swarm is not
yet known.
XVII
THE MAJOR METEOR SHOWERS—V
THE LOST STREAMS
IN the eighteenth and nineteenth centuries great meteoric streams of the
type already described in connexion with the Giacobinids and Leonids
were found to be associated with Biela’s Comet. After 1899, however,
the shower almost completely disappeared. This disappearance, together
with the strange disruption of Biela’s Comet, gives to the Bielid shower
a unique position in meteor astronomy. In more recent times a strong
shower associated with the Pons-Winnecke Comet has also disappeared.
No doubt many similar disappearances have occurred in the past, but the
two showers discussed in this chapter are the only prominent ones of
this type for which there is reliable information.
1. The Bielid (or Andromedid) shower
(а) History
In 1826 Biela discovered a faint comet, but when its orbit was com¬
puted it was realized that the same comet had been previously observed
by Montagno in 1772 and by Pons in 1805. The period of the comet was
6-6 years, and it was observed again in 1832 when it passed within 20,000
miles of the earth’s orbit. In 1839 the comet was unfavourably placed
and was not seen, but on 1845 December 29 Herrick and Bradley of
Yale saw a small companion comet beside the main one. The companion
comet grew in brightness and developed a tail. It seemed that violent
forces were disrupting the comet. At the next return in 1852 both comets
were faint and separated by over a million miles. They were last seen
in September 1852, and in spite of most careful searches were never seen
again on any subsequent return. In 1872 and 1885, however, when the
earth crossed the orbit of the vanished comet, there were tremendous
displays of meteors. Strong showers were also witnessed at the appro¬
priate times in 1892 and 1899, but since then no appreciable shower of
these Bielid meteors has been observed.
(б) Activity
The occurrences of prominent meteor showers connected with Biela’s
Comet have certainly been traced back to 174l,f while Klinkerfuest
t Olivier, C. P., Meteors (1925), ch. 7.
X Klinkerfues, W., OdUinger Nachrichten (April 30, 1873), p. 275, translated by W. J.
Fisher in Popular Astronomy, 39 (1931), 573.
360 THE MAJOR METEOR SHOWERS—V XVII, §1
brings forward arguments to show that the great shower and comet of
a.d. 524, together with other subsequent notable historic showers, might
have been associated with Biela’s Comet. Owing to the rapid regression
of the node, the dates of apparition of the shower show considerable
changes. Fisherf has investigated these changes in detail from 1741 to
1926 in order to predict the possible dates of future occurrences of the
showers. The available information on the activity and dates of appari¬
tion from 1741 is listed in Table 141.
Table 141
The Activity of the Bielid Stream
Source
Date
Kraflt (St. Petersburg)
.
1741 Dec. 6
‘Large number'
Brandos (Bremen) ....
.
1798 Dec. 7
~ 400/hour
‘Many*
Raillard (France) ....
Flaugerguee (Toulon)
Webb (England)
•
1830 Dec. 7
Herrick and Newton (U.S.A.)
Quetelet (Brussels)
1838 Dec. 6
100/hour
Heis (Aachen) ....
•
1847 Dec. 6
^ 150/hour
Zeziolo (Bergamo) ....
•
1867 Nov. 30
?
Many observers ....
•
1872 Nov. 27
Meteoric storm,
2,000-6,000/hour
Many observers (see Newton J) .
•
1885 Nov. 27
Meteoric storm,
75,000/hour ?
Many observers (see Newton§) .
.
1892 Nov. 23
'■** 300/hour
Denning||.
•
1899 Nov. 24
^ 100/hour
Donning ft.
.
1904 Nov. 21
~ 20/hour
Prentice .....
•
1940 Nov. 27-Dec. 4
6/hour
R. M. Dole (U.S.A.)§§
•
1940 Nov. 15
30/hour
The information about any appreciable return of the stream after
1899 is very uncertain. 01ivier|||| states that from the 1899 return until
1924 the number of Bielid meteors was insufficient to enable a radiant
to be determined, but Denningft gives an account of an apparent Bielid
shower observed in November 1904 both in Ireland and in Sweden.
Prenticehas described the attempts to observe Bielid meteors from
1921 to 1940. Nothing of interest was observed until 1940, when from
November 27 to December 4 definite Bielid activity was observed,
t Fisher, W. J.. Proc. Nat. Acad. Set. Wash. 12 (1926), 728, corrected in 13 (1927), 678.
X Newton, H. A., Amer. J. Sex. (3), 31 (1886), 409.
§ Newton, H. A., ibid. 45 (1892), 61.
|| Denning, W. F., Mon. Not. Roy. Astr. Soc. 60 (1900), 374.
ft Denning, W. F., ibid. 65 (1905), 851.
XX Prentice, J. P. M., J. Brit. Astr. Assoc. 51 (1941), 92.
§§ See note by Prentice, J. P. M., Brit. Astr. Assoc. Handbook (1947), p. 42.
III! Olivier, C. P., loc. cit.
THE LOST STREAMS
351
XVII, §1
although the rate was only a few per hour. In the same year, on November
15, R. M. Dole in the U.S.A. reported the occurrence of a fairly strong
shower of Bielid meteors. Radio-echo observations in 1946, 1947,f and
1948 J failed to record any significant activity from the Bielid radiant;
neither has there been any in the succeeding years up to 1953.§
Fio. 166. Tho curves of activity of the great Bielid meteoric
storm of 1872 Nov. 27.
As is the case with all the great meteoric storms which have been
observed, the duration of the Bielid displays of 1872 and 1885 was very
short, the earth passing through the dense part of the swarm in a few
hours. A curve of activity for the 1872 Bielid shower has been given by
Watson|| and is reproduced in Fig. 166. The behaviour of tho shower in
1885 was similar ; according to Newton|t the principal shower was over
in 6 hours. The much lower activity of the later returns seems to have
been more diffuse. Thus, according to Denning,the shower of 1899
was seen on November 23 and 24, and the Bielid meteors of 1904 from
November 16 to November 22. Since this shower occurred only 5 years
after tho 1899 return, and since the period of the comet is 6-6 years,
the comet was 15 months from perihelion and Denning inferred that
the meteors must be spread out over a considerable arc of the orbit.
The only subsequent observations, in 1940, confirm this dispersion of the
debris.
f Lovell, A. C. B., and Prentice, J. P. M., J. Brit. Astr. Assoc. 58 (1948), 140.
x Clegg, J. A., Lovell, A. C. B., and Prentice, J. P. M., ibid. 60 (1949), 25.
§ Jodrell Bank unpublished radio-echo observations.
|| Watson, F., Between the Planets (Blakiston, 1947), p. 127.
tt Newton, H. A., Amer. J. Sci. (3), 31 (1886), 409.
XX Denning, W. F. (1900), loc. cit.
362
THE MAJOR METEOR SHOWERS—V
XVII, § 1
(c) Radiant
A radiant position for the Bielid stream appears to have been first
given by Heis on 1847 December 6. This, and subsequent details of
radiant determinations, are listed in Table 142.
Table 142
Radiant Position of the Bielid Stream
Radiant
■Kl
Authority
Dote
a
5
1
Remarks
deg.
deg.
deg.
Heie.
1847
Dec. 6
(25
L 21
+ 40
54
• •
• •
• •
Zezioli .
1867
Nov. 30
17
48
..
• •
Newtonf .
1885
Nov. 27
24-54
44-74
several degrees
Mean of 90 radian te
DonningJ .
1899
Nov. 24
23
42-25
2-3
Elkin§ .
1899
Nov. 24
23-8
39-7
• •
One photographed meteor
Elkin ||
1905
Nov. 18
2501
46-08
• •
One photographed meteor
Denningft
1904
Nov. 21
/ 21
\ 26-03
50
44-16
• *
• •
("Nov. 30
23
44-5
2-5
4 meteors
Prentice $$
1940<
Dec. 2
29
45-6
7-5
6 moteors
[Dec. 4
23
41-5
0
4 meteors
The two photographic records m Table 142 were obtained by Elkin§ ||
during the initial photographic work at Yale. There are no published
records of any subsequent photographic determinations of the radiant.
(d) Velocities
As in the case of the other streams with well-marked periodicities, the
velocity of the Bielid meteors can be determined from the periodicity, the
expected geocentric velocity being 16 km./sec. The only photographic
velocity determination for comparison with this is the original one
obtained by Elkin§ in the work referred to above. His measured velocity
was 20-2 km./sec., which reduced to a geocentric velocity of 16-8 km./sec.
in reasonable agreement with the expected value. There are no records
of visual measurements of the velocity of Bielid meteors in Porter’s
analysis§§ of the British meteor data. During the radio-echo watch for
Bielid meteors in 1948|||| one velocity of 19-6±2-0 km./sec. was deter¬
mined. Although this is consistent with the uncorrected velocity of the
f Newton, H. A. (1886), loc. cit. $ Denning, W. F. (1900), loc. cit.
§ Elkin, W. L., Aatrophya. J. 12 (1900), 4. || See Olivier, C. P., Aatr. J. 46 (1937), 41.
ft Denning, W. F. (1905), loc. cit. XX Prentice, J. P. M. (1941), loc. cit.
§§ Porter, J. G.. Mon. Not. Roy. Aatr. Soc. 103 (1943) 134; 104 (1944), 257.
HU Clegg, J. A., Lovell, A. C. B., and Prentice, J. P. M. (1949), loc. cit.
THE LOST STREAMS
353
XVII, § 1
Bielid meteors, little weight can be attached to it since the radiant is
unknown.
(e) Orbit
According to Olivier,t both Weiss and d’Arrest announced almost
simultaneously in 1867 that the Andromeda meteors moved in the orbit
of Biela’s Comet, the history of which has been referred to above. Weiss,
in 1868, clearly pointed out the effect of the rapid decrease in the longitude
of the node and predicted that the shower of 1872 should occur about
November 28, not in December as the previous returns had done. The great
meteoric storm of 1872 November 27 confirmed this prediction. Table
143, compiled from data given by Olivier,t lists Newton’s positions for
the node and inclination of the comet’s orbit, and Hind’s values for the
minimum distance between the orbits of the earth and the comet at the
various returns. (Since the comet disappeared in 1852, the figures for
1859 and 1866 are predictions only.)
Table 143
The Changes in the Orbit of Biela's Comet
Date
SI
.
Distance
(comet orbit-earth orbit)
Sun's longitude O on
dates of occurrence of
Bielid showers
deg.
deg .
a.u.
Date
deg.
1772
258*7
17
-0*06545
• •
..
• •
• •
1798
256*2
1806
252*4
13 6
+ 001321
• •
• •
1826
251*2
13*6
+ 0*00892
• •
• •
1832
• •
• •
+ 0*00087
• •
• •
1833
249*0
• •
13*2
• •
1838
256*1
1839
• •
-0*00009
• •
• •
1846
246*5
12 6
-0*01680
• •
• •
..
• •
1847
257*7
1852
246*3
12*6
-0*01130
• •
• •
1859
246*1
12*4
+ 0*00567
..
• •
1866
• •
• •
246*0
• •
12*0
• •
+ 0*01295
• •
1867
1872
248*4
246*1
••
1885
245*8
The consistency between the changes in the orbit of the comet and the
times of apparition of the shower is apparent from Table 143.
The close connexion between the orbital elements of the meteor stream
observed in 1885 and those of the comet was shown by Corrigan]: in
1886. His data are given in Table 144.
f Olivier, C. P., Meteors, ch. 7.
X Corrigan, S. J., Sidereal Messenger, 5 (1886), 144 (see Olivier, loc. cit.).
a a
3605.60
354
THE MAJOR METEOR SHOWERS—V
XVII, §1
Table 144
Orbital Elements of Biela’s Comet and the Associated Meteor Streams
Authority
Long, of
Perihelion
rr
Long, of
node ft
i
Perihelion
distance
e
(o.w)
Co nigant
Biela'a Comet .
109° 40'
246° 29'
12* 33'
0-8606
0-7669
3-626
*»
Metoor stream
1885 Nov. 27 .
108° 16'
245° 67'
13° 08'
0-8578
Ellon*
Single meteor
• •
1899 Nov. 24 .
108* 48'
242* 22'
12* 04'
• •
0-7923
4-110
Prentioo§
Nov. 1940.
109*-3
250 # -7
!3*-2
0-875
0-767
3-6
The only determination for an individual meteor is that given by
Elkin, X which agrees well with the cometary elements. Also given
in Table 144 are the elements for the stream observed by Prentice§ in
1940, which is in good agreement with the elements of the comet.
This agreement is in many ways somewhat surprising, since the ob¬
servations made by Prentice were from November 27 to December 2,
whereas, according to the rapid regression of the node observed in the
nineteenth century, the shower would have been expected to occur in
early November. Prentice believes that there may now be several
meteoric currents associated with Biela’s Comet, as indeed was suggested
by Klinkerfues|| in 1873. The remarkable history of the comet and of
the associated meteor streams lends particular interest to future observa¬
tions of any return of the Bielid meteors.
2. The Pons-Winnecke meteors
(a) History
On 1819 June 12 Pons discovered a new comet, and although its period
was computed as 5-62 years it was not until 1858 March 8 that it was
rediscovered by Winnecke. Since then it has been regularly observed.
The aphelion of the comet’s orbit lies very close to Jupiter, and since
the period of the comet is almost exactly half that of Jupiter it suffers
considerable perturbations at each alternate revolution. These perturba¬
tions brought the orbit of the comet very close to that of the earth. On
1916 June 28 the orbit was, in fact, only 3 million miles from the earth
and a strong shower of meteors was observed. Subsequently the per¬
turbations increased the separation of the orbits, and although there are
records of meteors from the shower during the 1921 and 1927 returns
the shower is now regarded as completely lost.
t Corrigan, S. J., loc. cit. (see Olivier, loc. cit.).
X Elkin, W. L. (1900), loc. cit.
§ Prentice, J. P. M. (1941), loc. cit. || Klinkerfues, W. (1873), loc. cit.
XVII, §2
THE LOST STREAMS
365
(6) Activity
The only appreciable display of the Pons-Winnecke meteors occurred
during May and June 1916. A very sharp maximum seems to have
occurred on 1916 June 28, which was seen by observers in Englandf but
not in America. Denningf gave the rate as 32 per hour, but other
observers gave 100 per hour, whereas in America the rate did not exceed
6 per hour. 01ivier§ gives details of the low hourly rate of meteors belong¬
ing to this shower from 1916 May 20 to July 10. The disparity in the
rates observed in England and America on June 28 indicates that the
dense part of the swarm must have been extremely localized since only
6 hours elapsed between the English and American observations.
The expectations of a great display when the comet returned to
perihelion in 1921 were not fulfilled. Very few Pons-Winnecke meteors
were observed either in England or in America, although the Japanese
observer8|| reported a strong shower of very faint meteors. At the next
return in 1927 the only reports of significant numbers of Pons-Winnecke
meteors came from Russiaff and from DoleJJ in America. There are
no further accounts of observations of this meteor stream.
(c) Radiant
The observed radiant positions as collected by 01ivier§ for the 1916
shower are given in Table 145.
Table 145
Radiant Positions of the Pons-Winnecke Shower 1916
Source
Date
Radiant
a S
No. of meteors
A.M.S.§§
1916
May 21 6
deg. deg.
224-5 +25-3
8
May 26-68
2303
27-4
7
• •
May 27-25
231-0
27-5
7
M
May 27-67
232-1
26-8
4
99
May 30-14
232-7
28
15
99
June 3-7
234-4
27-5
16
9f
June 4-68
235-8
25-6
9
British observers
Juno 28-5
203
53
100
Denning
June 28-5
231
54 \
69
*»
Juno 28-5
223
41 /
A.M.S. .
July 3-67
206-7
61-2
5
t Nature, 97 (1916), 388.
j Donning, VV. F., Observatory, 36 (1916), 356.
§ Olivior, C. P., Mon. Not. Roy. Astr. Soc. 77 (1916), 71.
|| Kyoto Publications, 5, no. 5; Observatory, 45 (1922), 81.
ft Observatory, Nov. 1927. Dole, R. M., Observatory, 51 (1928), 25.
§§ American Meteor Society.
356 THE MAJOR METEOR SHOWERS—V XVII, §2
It appears from these observations that a number of distinct radiants
were active simultaneously, especially on the night of maximum, June
28. The connexion between these various groups was investigated by
Smith,t who computed an ephemeris for the A.M.S. radiants determined
in late May and early June for comparison with the theoretical Pons-
Winnecke radiant and with the British radiants of June 28. His epheme-
rides are given in Table 146.
Table 146
Ephemeris of the Pons-Winnecke Radiant
1916
SI
Ephemeris of the
A.M.S. radiant
(parabolic elements)
Ephemeris of the
A.M.S. radiant
( elliptical elements)
Ephemeris of Pons-
Winnecke radiant
May 21
m
!l+<u= 283° 24'
a 5
229° 04' 25° 60'
Sl+ cu = 287° 36'
a 8
227° 55' 22° 48'
Sl+u> =■ 271° 36'
a 8
222° 39' 33° 62'
31
231 36
29 38
228 66
29 43
222 49
40 19
June 10
232 30
35 03
228 45
35 57
221 00
46 68
20
na
231 11
40 34
226 55
41 18
216 41
60 37
30
KXl
227 07
45 36
222 43
45 37
209 22
63 24
July 10
107 62
220 08
49 13
216 63
48 11
200 31
64 24
Smith concludes that the A.M.S. radiants of late May and early June
would have drifted with time towards the British radiants of June 28
and to the theoretical position of the Pons-Winnecke radiant. Even
so, the agreement is not good, and since the node differs by 30° it seems
that the meteors must have been separated from the orbit of the comet.
(d) Velocities and Orbit
There are no records of any velocity determinations of the Pons-
Winnecke meteors, and the orbital data have therefore been computed
by assuming either parabolic or elliptical elements. As regards the orbit
of the comet, it has been subject to unusually severe perturbations as
mentioned above, owing to its close approach to Jupiter at aphelion. The
changes in the elements from 1858 to 1945 have been listed by Porter X
as in Table 147.
In 1916 the perihelion point was inside the earth’s orbit, but successive
perturbations then caused the perihelion point to move outside the orbit,
and the distance has now increased so much that further occurrences of the
Pons-Winnecke meteor shower seem extremely unlikely. The connexion
t Smith, F. W., Mon. Not. Roy. Astr. Soc. 93 (1932), 166.
j Porter, J. G., Rep. Phys. Soo. Progr. Phya. 11 (1948), 402.
XVII, §2
THE LOST STREAMS
357
Table 147
Changes in the Orbital Elements of the Pons-Winnecke Comet
Date
SI
i
o
q
Distance
( comet-earth)
Computed, radiant
a 5
1858
113-5°
10-8°
0-755
(o.u.)
0-709
(a.u.)
-0-231
deg.
• •
deg.
• •
1880
104-1
14-5
0-720
0-885
-0-128
204
+ 45
1915
99-4
18-3
0-701
0-972
-0-041
208
54
1921
98-1
18-9
0-078
1 041
+ 0-030
205
57
1939
90-8
20-1
0-070
1102
+ 0-092
205
69
1945
94-4
21-7
0-054
1100
+0-150
207
00
of the meteor stream observed in 1916 May-June with the Pons
Winnecke comet was pointed out by Denningf and by Olivier.J The
possibility of reconciling the various radiants observed with the single
cometary orbit has been discussed above.
t Donning, W. F., Observatory, 40 (1917), 95; Nature, 97 (1910), 388, 457.
X Olivier, C. P., Circ. Harv. CoU. Obs. (1916), p. 614; Afon. Not. Roy. Astr. Soc. 77
(1910), 71.
XVIII
THE MAJOR METEOR SHOWERS—VI
THE DAY-TIME STREAMS
(a) History
The evolution of the radio-echo technique for the study of meteors
enabled a systematic survey to be made of meteoric activity, unhampered
by cloud or daylight. The day-time results were of particular interest
since they yielded the first information about the meteor streams falling
on the sunlit side of the earth. During the summer of 1945 Hey and
Stewart f delineated two day-time radiants between June 6 and 13, and
during the daylight hours of 1946 May, June, and July, Prentice, Lovell,
and Ban well J found a high general level of meteoric activity. At that
time the real significance of the results was not apparent, since little
evidence existed of the relation between the number of radio echoes
and the number of visible meteors. During the autumn and winter of
1946-7 the workers at Jodrell Bank made a careful survey of the known
meteor showers, from which it was apparent that, with the particular
apparatus in use, a close relation existed between the number of radio
echoes and the number of meteors seen by a visual observer. The results
obtained with this apparatus in daylight were not exceptional until May.
Then, during the investigation of the rj -Aquarid shower on 1947 May 1,
it was found that the well-known shower with its radiant near 77 -Aquarii
was not an isolated event, but merely the beginning of a great belt of
meteoric activity extending towards the sun, observable only in daylight.
Initially the main radiant was in Pisces, but the phenomena developed
with great rapidity, and by the end of June at least seven centres of
considerable activity had been delineated, extending in the ecliptic up
to right ascension 90°. The day-time activity continued throughout July
and August, and comparison with the known major showers indicated
that it was without precedent in extent and duration. Preliminary
announcements of the discovery of this remarkable activity were made
on 1947 June 26§ and September 18,§ and a full acount of the observations
was given by Clegg, Hughes, and Lovell.|| In subsequent years much
f Hoy, J. S., and Stewart, G. S., Proc. Phys. Soc. 59 (1947), 858.
X Prentico, J. P. M., Lovell, A. C. B., and Banwell, C. J., Af on. Not. Roy. Astr. Soc.
107 (1947), 155.
§ Lovell, A. C. B., Brit. Aatr. Assoc. Circ. (June 26, 1947), no. 282; (Sept. 18, 1947),
no. 285.
|| Clegg, J. A., Hughes, V. A., and Lovell, A. C. B., Mon. Not. Roy. Astr. Soc. 107
(1947), 369.
OKQ
XVIII THE DAY-TIME STREAMS
more detail was obtained about this day-time activity. The 1948 observa-
tionst showed that the main phenomena were recurrent, and prehminayy
velocity measurements were made.J In 1949 and 1950 the orb.ts of the
main streams were first clearly delineated,§ and these results were con¬
firmed in 1951|| and 1952.|t It is now clear that the dominant s ‘ reams °*
the summer sequence are the Arietids and 5-Perseids in early June, and
the fi-Taurids in late June. These have returned in great strength in each
year of observation and their orbital characteristics are now well
established. A number of other less active streams—apparently not all
recurrent-have comprised the activity in May and July. Unless
otherwise stated, the account in this chapter is a survey of the original
papers from Jodrell Bank referred to above.
Fio. 167. Rango-time plots of echoes with aeriol directed at
azimuth 90° on 1947 May 7 showing the well-known ij-Aquarid
shower in transit at 07h. 40m. and the day-timo shower in Pisces
at lOh. 40m.
(6) Activity
The original investigation in 1947 was made with a single directional
aerial, and one of the early range-time plots (see Chap. IV), which indi¬
cated beyond doubt the existence of a new series of showers, is shown
in Fig. 167. This figure contains the results with the aerial directed at
azimuth 90° on May 7 between 07h. 20m. and 13h. 20m. The ij-Aquarids
transited at 07h. 40m., and after some scattered activity another clearly
defined radiant passed through the beam at lOh. 40m. The activity of
this new radiant (which was found to lie in Pisces) at that stage was 13
per hour, or twice the activity of the ^-Aquarids. After early May, in
each year, a very rapid increase in activity has occurred. The extent of
this is well indicated by the range-time plots shown in Fig. 168 covering
f Aspinall, A., Clogg, J. A., and Lovell, A. C. B., ibid. 109 (1949), 352.
t Ellyett, C. D., ibid., p. 359. .
§ Aspinall, A., and Hawkins, G. S., Mon. Not. Roy. Astr. Soc. Ill (1951), 18; Davies,
J. G., and Greonhow, J. S., ibid., p. 26; Almond, M, ibid., p. 37.
|| Hawkins, G. S., and Almond, M., Jodrell Bank Annals, 1 (1952), 2.
ff Almond, M., Bullough, K., and Hawkins, G. S., ibid., p. 13.
Fio. 168 (a)
MANOC (AMS )
Fio. 168 (c)
Fio. 168. Portions of the range-time plots covering the period of the Arietid and
C-Pereeid streams in 1950 June. The apparatus used was the radiant-survey
apparatus described in Chapter IV: and the plots are those for the twin aerials
for each day.
XVIII
THE DAY-TIME STREAMS
363
the period of activity of the Arietids and £-Perseids in June 1950 as
measured on the radiant-survey apparatus (Chap. IV). In interpreting
these records it must be remembered that the rate is equivalent to that
which would be visible to a single observer under good dark-sky condi¬
tions. In each year the richest stream of the sequence has been the
Arietids, and the outstanding activity and duration of the shower may
1949 Dec.
F10. 169. Comparison of tho mean hourly rates of tho night time Geminid
showor in 1949 Decombor, and tho day-time Arictid shower in 1950 June.
be seen from Fig. 169, where the mean hourly rates are compared with
those for the well-known night-time Geminid shower (Chap. XV). The
general levels of activity for the summer months of 1947, 1948, and 1950
are shown in Figs. 170(a), (6),(c), respectively, while Fig. 170(d) shows
the corresponding night activity for comparison.
With the methods of recording used with the single-aerial equipment
in 1947-9 it was not possible to determine the daily activity of the
individual radiants, but maximum hourly rates could be assigned and
are given in Table 148,f which also contains the detailed rates of the
individual radiants for 1950-2.
t Tho results for 1949 were somewhat meagre owing to the fact that the equipment
was in process of change from the single-aerial working to the twin aerials of the meteor-
survey equipment. Tho broad features of the activity, dominated by the Arietids, were
sfcill apparent.
May June July ' August 194 7
Fio. 170 (a). Moan hourly rat* per radiant 1947 May-August.
Ordinate*: number of echoes per hour.
4 B U /6 /O ** * \l S 9 IS 17 21 2S Z9 3 7 II IS t) IS 17 St 4 0 7} 16 ?0 14 29
Mag June July August 19 48
Fio. 170 (6). Mean hourly rate per radiant 1948 May-August.
Ordinates: number of echoes per hour.
Fio. 170 (c) and ( d ). The day- and night-time metoor activity during the
summer of 1950.
Ordinates: 170 (c). Maximum hourly rate of echoes during day-time 06h. OOra.-
18h. OOra. U.T.
Ordinates: 170 (d). Maximum hourly rate of echoes during night-time 18h. 00m.-
06h. 00m. U.T.
366
THE MAJOR METEOR SHOWERS—VI
Table 148
Activity of the Day-time Meteor Radiants
XVIII
Stream
Tj-Aquarida
Pisoida
May 1
May 4
May 6
May 7
The original Piacid atroam
waa not delineated in 1960-2
v-Piscids
o-Cotida .
May 12
13
Arietidaf
£-Pereeida
May 29
30
31
Juno 1
2
3
4
6
6
7
8
9
10
11
12
13
14
16
16
17
18
June 1
2
3
4
6
6
7
The t'-Piacida and the
o-Cetid atreama were not de¬
lineated in 1947-8 but may
have been associated with
the minor atreama which
were thon found to be con¬
nected with the 1947
Piacids.
• •
12
Not
••
16
delineated
18
23
• •
26
Not
18
• •
dolineated
• •
18
22
• •
18
• •
• •
25
13
• •
18
• e
18
16
21
20
16
32
36
22
23
39
37
39
41
27
35
31
24
40
41
12
72
30
34
76
67
34
64
31
43
49
37
• •
e •
23
30
48
23
44
48
32
22
46
38
19
18
22
20
30
19
• •
26
16
12
s s
14
• •
35
20
23
13
20
23
15
39
# ,
15
29
17
29
18
• •
20
20
32
28
22
33
37
23
39
32
16
29
48
17
• •
..
• •
33
26
t In the publication of the 1947 results the Arietid stream was labelled Stream D. In the
publication of the 1948 results this Arietid stream was wrongly interpreted as consisting of two
radiants labelled D (( -Perscida) and H (Arietida). The close proximity of two suoh active streams
as the Anotids and {-Perseida made the interpretation diffioult until the meteor-survey apparatus
became operative in 1950.
XVIII
THE DAY-TIME STREAMS
Table 148 (cont.)
Activity of the Day-time Meteor Radiants
367
Stream
Date
1947
1948
£.Peraeida
June 12
In tho publication of tho
(cont.)
13
1947 reaulte tho f-Poreeids
14
wore labelled
stream E |
16
and in the 1948 result*
16
stream D\
64-Porscids
Juno 21-9
60 (June 26)
36 (Juno 26)
/J.Taurid9.
June 24
..
• •
26
• •
• •
26
e •
• •
27
06
• •
28
# #
• •
29
• «
• •
30
• •
• •
July 1
• •
• •
2
• •
• •
3
• •
36
4
• •
• •
6
• •
• •
a-Orionid* . ,
July 12-17
Not dolineatod
60 (July 12)
v-Gorainids
July 12-17
Not delineated
60 (July 12)
A-Geminida
July 12-17
Not delineated
32 (July 12)
0-Aurigids
July 23-
Aug. 4
Not delineated
20 (July 26)
1950
19
12
7
9
1961
1962
14
u
15
14
12
19
29
21
20
38
24
14
22
Not dolinoatod
10
11
24
16
21
23
17
14
19
24
19
Not dolinoatod
Not dolinoatod
Not dolinoatod
Not dolinoatod
28
16
29
21
26
26
Since 1950 the activity of these streams has been obtained from the
range-time plots by a standardized method which makes direct com¬
parison possible between the activities in the various years. The meteor
rates are standardized by comparison with the sporadic activity over the
period of the individual shower. The only assumption in this standard¬
ization is that the density of sporadic meteors is constant at any
particular position of the earth’s orbit. The 1950 conditions, which gave
a radio-echo rate comparable with the visual rate for a single observer
during the major night-time showers, has been taken as standard. In
that year the mean hourly rate of sporadic meteors was 6-3 for the
Arietid and Perseid epochs and 9-6 for the Taurid epoch, and these now
form the standard of comparison.
It will be evident from Table 148 that the major sequence of the
Arietids, £-Perseids, and /3-Taurids has recurred over the five years of
the investigation. The activity in mid-May and during July is very con¬
fused, however, and although the general level of the activity has
remained consistently high during these epochs there has been no similar
368
XVIII
THE MAJOR METEOR SHOWERS—VI
consistency in the coordinates of the radiants delineated. The original
Piscid stream of 1947 and 1948 May was not in evidence on the 1950,
1951 records, which, however, showed radiants near v-Piscium ando-Ceti.
On the 1952 records none of these radiants could be delineated. The
major 54-Perseid stream was found only in 1947 and 1948 and the four
streams, ot-Orionids, i/-Geminids, A-Geminids, 0-Aurigids, of July only
in 1948. Further investigations in subsequent years will be required
before it can be ascertained whether these streams are moving in long-
period orbits or whether they represent isolated occurrences.
Fio. 171 (a). The radiant positions of tho 1950 day-time raotoor streams shown
on a Mercator projection. Individual radiant positions are plotted for tho
Arietids, q-Aquarids, and o-Cotids. The diameter of a radiant represents the
probable error in its position. For tho {-Perseids and /J-Taurids the weighted
moan position is given, and the area shows the scatter of the radiant* in oach
group.
(c) Radiants
The radiants of the streams in 1947 and 1948 were delineated by using
the single movable aerial. With this technique it was rarely possible to
measure both right ascension and declination on the same day. Since
1950 the radiant-survey apparatus has been in operation, and this must
be regarded as giving the more precise information. The full information
on the mean radiant positions is given in Table 149, while Table 150
contains the day-to-day radiant determinations of the streams delineated
since 1950.
The radiant positions of the streams measured in 1950-2 are shown on
the Mercator projections in Figs. 171 (a), (6), (c). Similar diagrams for the
radiants of the 1947 and 1948 results have been given in the appropriate
publications. The sequence of radiant positions for the Arietid stream
XVIII
THE DAY-TIME STREAMS
369
given in Table 150 shows a definite eastward trend in right ascension
with an abnormal motion away from the ecliptic. The daily change in
coordinates has been deduced by using a weighted least mean-square
Fio. 171 (6). Tho radiant positions of the 1961 day-timo meteor atroams ahown
on a Mercator projection. Individual radiant positions aro plotted for the
Arietida, the area of a radiant representing the probable error in its position.
For other streams tho weighted mean position is givon and tho area shows the
scatter of the radiants in each group.
ISO' no' too’ 9 o' 80' 70* 60* SO' 40' SO' SO-
Right Ascension
O' 330' S40- 330' 320'
Fio. 171 (c). The radiant positions of the 1952 day-timo moteor streams
shown on a Mercator projection. Individual radiant positions are plotted for
the Arietids; otherwise the weighted mean position is given and tho area shows
the scatter of the radiants in each group.
method and the ephemeris of the radiant obtained from the combined
1950-2 results is given in Table 151. The radiant of the £-Perseid stream
also shows a pronounced eastward trend with abnormal motion away
from the ecliptic. In the case of the /1-Taurid stream the eastward trend
b b
8595.86
370 THE MAJOR METEOR SHOWERS—VI
XVIII
XVIII
THE DAY-TIME STREAMS
371
Table 150
Daily Radiant Positions of the Day-time Streams 1950-2
Stream
Date
1950
1951
1952
Radiant
a 8
Radiant
diameter
Radiant
a 5
Radiant
diameter
Radiant
a 8
Radiant
diameter
deg.
deg.
deg.
deg.
deg. |
deg.
deg.
deg.
deg.
ij-Aquarida .
May I
•
•
• •
313
-4
< 3
•
4
•
.
• •
• •
* *
• •
330
-2
< 3
0
338 5
+ 3 0
< 3
••
"
• •
•
• •
v-Piaoida
May 12
• •
• •
..
15
+ 28
6
• ■
13
• •
••
• •
17
+ 26
8
• •
o-Cotida
14
27-5
-3 5
< 3
20
+ 4
7
• •
15
. .
• •
• •
26
-8
< 3
• •
16
..
..
..
..
• •
17
..
• •
• •
38
-3
11
• •
18
28-5
00
< 3
..
• •
• •
10
• •
• •
. #
• •
• •
• •
• #
20
• •
• •
• •
• •
• •
• •
• •
21
29 6
-60
10
• •
• •
• •
c •
22
mm
mm
• •
• •
• •
• •
23
121
Hull
• #
• •
• •
• •
KB
IPS#
+
+
Ariotids
May 29
far
42
20
4
36
17 ;
3
30
UK
mm
H
43
23
4
..
• •
31
43 0
260
< 3
43
20
< 3
38
14
< 3
Juno 1
43 0
270
< 3
39
28
< 3
40
15
< 3
2
39 0
160
< 3
38
20
3
41
17
< 3
3
39-6
18 5
< 3
42
22
4
42
14
3
4
425
17-5
< 3
41
22
3
42
16
< 3
5
41-5
200
< 3
41
20
< 3
43
17
< 3
0
420
210
< 3
44
26
< 3
46
23
3
7
44 5
235
< 3
44
27
< 3
46
23
< 3
8
46-5
21 0
< 3
42
26
< 3
48
24
< 3
9
460
260
< 3
45
26
3
45
23
< 3
10
48 5
23-6
< 3
No record
No rocord
11
460
20-5
< 3
45
26
3
47
24
< 3
12
46-5
250
< 3
45
21
3
49
23
< 3
13
480
270
< 3
46
27
3
61
29
3
14
45
23
4
51
24
3
15
Position not deter-
47
27
3
48
29
< 3
10
mined
owing to solar
..
• •
51
24
< 3
17
radio
noiso
intorfer-
49
29
8
..
• •
18
enco
..
..
51
24
4
19
• .
• •
..
47
25
3
+
+
{•Perseids .
June 1
580
280
< 3
55
8
7
68
26
0
2
67-5
270
< 3
65
17
5
63
25
4
3
53-6
19 5
< 3
..
..
..
69
28
8
4
58-5
14 0
< 3
66
14
3
66
18
< 3
5
60-5
24 0
< 3
• •
..
..
59
23
4
6
54-5
23-6
4
69
28
8
63
23
7
7
620
250
3
61
20
4
60
19
3
8
63-5
200
< 3
62
22
9
02
27
9
9
660
250
< 3
66
33
8
60
15
5
372
THE MAJOR METEOR SHOWERS—VI
Table 150 (cont.)
XVIII
Stream
Date
1950
1961
1952
Radiant
a 8
Radiant
diameter
Radiant
a 8
Radiant
diameter
Radiant 1
a 8
Radiant
diameter
{-Peraeids
deg.
deg.
deg.
deg.
deg. 1
deg.
deg.
deg. 1
deg.
10
63-6
230
< 3
No record
No roc
ord
(con/.)
11
• •
• s
• •
66
29
11
03
+ 23 1
6
12
62-5
220
< 3
06
28
8
67
+ 24
7
13
..
..
..
65
33
9
Radiant ill
•defined
14
69-6
240
< 3
61
18
4
16
720
280
3
70
18
8
69
+ 21
3
10
71-5
29 6
< 3
• •
• •
..
• •
17
• •
• •
• •
••
••
••
73
+ 23
3
/J-Taurida .
Juno 24
80
15
< 3
• •
• •
26
• •
• •
• •
80
16
< 3
• •
• •
• •
26
805
150
< 3
80
16
< 3
81
+ 13
3
27
87-6
170
< 3
89
18
3
86
+ 13
6
28
860
190
< 3
85
21
6
88
+ 17
6
29
88-6
240
< 3
• •
..
..
• •
30
80 0
26-6
< 3
87
20
• •
90
+ 26
3
July 1
85 5
21 0
< 3
87
19
< 3
90
+ 22
< 3
2
805
17-5
7
88
29
4
83
+ 16
4
3
86 5
17-5
5
89
26
6
• •
• •
4
88-6
130
< 3
91
21
8
• •
• •
• •
6
• •
• •
••
88
20
4
••
• •
is again evident, but the motion is toward the ecliptic. The ephemerides
for these streams, obtained as above, are also included in Table 151. The
mean daily motion of the Arietid radiant is Aa = +0°-7, A8 = -f 0°-6;
for the J-Perseids Aa = +1°*1, AS = + 0°-4, and for the /?-Taurids
Aa = +0°-8, AS = + 0°-4.
(d) Velocities
The first velocity measurements of the day-time streams were made
in 1948, when between June 25 and August 6 the velocities of sixty-one
meteors were obtained using the radio-echo diffraction technique. Un¬
fortunately, this covers a period of confused activity, and with the single
aerial then in use the identification of the measured meteors with
specific streams presented some difficulty. The homogeneous groups
which were identified appeared to relate to the 54-Perseid and 0-Aurigid
streams for which apparent geocentric velocities of 37-5±3-7 km./sec.
and 32-9±2-7 km./sec. were obtained respectively. These values gave
approximate heliocentric velocities of 39-1 ± 2-6 km./sec. for the 64-
Perseids and 27-5±l-4 km./sec. for the 0-Aurigids, indicating that the
orbits of the streams were elliptical. As these two streams have not been
identified in subsequent years, it has not been possible to confirm the
results.
With the introduction of the twin-aerial survey equipment for
Table 151
Z t ot Z SZ Z9Z VfZ * ' 0S6I ^nf-ounp :
Apif OUTlf
374
XVIII
THE MAJOR METEOR SHOWERS—VI
radiant measurement, the single-aerial system was directed exclusively
to the measurement of velocities during the summer day-time period.
In 1949 the measurements could only be made between May 30 and
June 18, during which time twenty-two velocities of Arietid meteors
were obtained, giving a mean velocity of 38-5±4-0 km./sec. In 1950 a
full programme of measurements was carried out which resulted in
velocity determinations for the o-Cetids, Arietids, £-Perseids, and p-
Taurids. In 1951 the velocities of the Arietids and £-Perseids were
determined again, while the 1952 measurements yielded results for the
Anetids and /1-Taurids. The details for the various streams are given
below, and the results summarized in Table 152.
Fio. 172. Distribution of o-Cetid velocities, 1950.
(i) o -Cetids. The velocity of thirty-seven o-Cetid meteors was
measured between 1950 May 13 and May 23. The distribution is shown
in Fig. 172, the mean velocity being 36 a 7±4*2 km./6ec.
(ii) Arietids. The measurement of the Arietid velocities presents some
difficulty because of the proximity of the radiant to that of the J-Perseid
radiant, the separation in right ascension being only 20 degrees. During
the period of early June, when both streams are highly active and when
it is necessary to measure the velocities of both streams, a special tech¬
nique has been employed. Whereas normally the radiant can be followed
by a single movable aerial, in this case the aerial is maintained on a fixed
azimuth during the transit of both radiants. Range-time plots are then
made of the echoes yielding velocity measurements as shown in Fig. 173.
The selection of velocities for each radiant is made by taking those which
fall within the appropriate range-time envelopes. Fig. 173 shows the
XVIII
376
THE DAY-TIME STREAMS
results of this technique over the period 1950 May 31-June 12. The
Arietid envelope contained forty-four velocity measurements and the
Hours f U T)
Fia. 173. Rongo-tirao distribution of echoes giving velocity determinations
(1950 May 31-June 12).
x Arietid echoes, o {-Poreeid ochoes. -theoretical range-time distributions.
Velocity t km /sec. I
Fio. 174. Distribution of 122 Arietid velocities, 1950.
J-Perseid envelope twenty-one. In this year after June 12 the aerial
was moved to follow the Arietid radiant between June 12 and 16,
giving a further seventy-eight velocities. The distribution of the 122
velocities is shown in Fig. 174, the mean being 37-7^4-3 km./sec. The
same technique was employed in 1951 and 1952 with similar results.
376
THE MAJOR METEOR SHOWERS—VI XVIII
(iii) l-Perseids. The measurement of the £-Perseid velocities has
been referred to above, and the results for 1950 are included in Fig. 173.
The appropriate histogram of the twenty-one {-Perseid velocities is
shown in Fig. 175(a), and that of the twelve measured in 1951 in
Fig. 175(6). The velocity of the stream was not determined in 1952.
Fig. 175. (a) Distribution of {-Persoid Flo. 176. Distribution of /J-Taurid
velocities, 1950. (6) Distribution of velocities, 1950, 1952.
(•Perseid velocities, 1951.
(iv) p-Taurids. The velocities of ten /3-Taurid meteors were deter¬
mined in 1950. No measurements were obtained in 1951, but in 1952 a
further eleven velocities were obtained. The combined results are
shown in Fig. 176.
The velocity distribution for each of these showers shows an appreci¬
able spread about the mean. This is partly due to the unavoidable
inclusion of sporadic meteors in the group, but, even for the Arietid
radiant where the shower rate is greatly in excess of the sporadic rate,
the spread remains large. In the 1950 observations the r.m.s. error for the
individual determinations in the Arietid group was 2-4km./sec., while
the standard deviation of the group was 4-3 km./sec. Hence there must
exist a considerable true spread in the velocities of individual meteors
in these groups. The significance of this is discussed below.
(e) Orbits
After the discovery of the day-time streams, the delineation of their
orbits became a matter of great interest. Both Hoffmeisterf and
t Hoffraeister, C., Forachungen und FortschriUe (Oct. 1947), nr. 19/20/21; DieMeteor-
etrihne.
XVIII
377
THE DAY-TIME STREAMS
Table 152
The Velocity Measurements of the Summer Day-time Streams
' N \ Stream
o-Cetids
Arieiida
Peroeida
Year
—
Number
v±dv
km./sec.
Number
v±dv
km./aec.
Number
v±dv
km./aec.
1948
• •
..
• •
..
• •
1949
..
22
38-5±40
• •
• •
1950
37
36-7±4-2
122
37-7±4-3
21
28-8±3-2
1951
..
• •
39
38-7±4-4
12
29 0±3-9
1962
••
• •
28
38-5±3-2
• •
• •
x. Stream
Year
54 -Peraeida
/?•Taurida
0-Aurigida
Number
v±dv
km./aec.
Number
v±dv
km./aec.
Number
v±dv
km./aec.
1948
15
37-5±3-7
• •
• •
6
32-9±2-7
1949
• •
• •
• •
• •
..
• •
1950
• •
• •
10
31-4±41
..
• •
1951
• •
• •
• •
• •
• •
1952
• •
• •
11
31-5±2-7
• •
• •
Whipplef had independently suggested that meteor streams moving
in short-period orbits might give rise to showers incident on the sunlit
hemisphere of the earth. In fact, we have already mentioned in Chapter
XV that from the detailed study of the orbit of the November Taurids,
Whipple predicted that the Taurid orbit should intersect the earth’s
orbit after perihelion passage ‘producing only day-time meteors unlikely
to be observed except as fireballs in late June and early July’. It was
realized in 1947 that the radiant of the /3-Taurid shower of late June
was most probably the day-time return of the autumn Taurids, and this
was confirmed when it became possible to calculate the orbit in 1950.
The preliminary velocity measurements made in 1948 for the 54-Perseid
and 0-Aurigid streams indicated that the orbits were of short period, but
little precise information was obtained until the more comprehensive
measurements of 1950 gave data for the o-Cetid, Arietid, £-Perseid, and
/3-Taurid streams. The information obtained in the years 1950-2 is
summarized below.
(i) o-Cetids. It has only been possible to calculate the orbit of this
shower from the 1950 observations and the details are given in Table 153.
The observed radiant has been corrected for zenith attraction and
diurnal aberration. The shift in ASl was not sufficient to produce a
f Whipple, F. L., Proc. Amer. Phil. Soc. 83 (1940), 711.
378
THE MAJOR METEOR SHOWERS—VI
XVIII
detectable change in velocity and the orbit is computed from the mean
radiant and velocity. The mean date has been used to determine the
node. The spread in the elements was estimated from the radiant move¬
ment and velocity spread. The velocity spread primarily determines
Aa, Ae, and Aq; Ai is influenced both by Av and by Aa, and Aw primarily
by Aa. The orbit of this stream projected on to the plane of the ecliptic
Fio. 177. Orbits of summer day-time metoor streams projected on to tho piano
of the ecliptic.
is shown in Fig. 177. Since oj is 211° and i 34°, the orbit does not approach
the earth except in May.
(ii) Arietids. It has been possible to compute the elements of the
Arietid orbit in each of the years 1950-2, and the results are given in
Table 154. The details of the corrections and the estimates of the spread
are as described for the o-Cetids. The radiant shows a steady change
in right ascension and declination, and orbits for the first and last dates,
with the same semi-major axis as the mean orbit, have been computed
from the smoothed radiant positions. Although the shape remains
almost unchanged, both i and n vary with position in the shower, and
the line of apsides swings gradually forward.
The mean orbits for the various years agree satisfactorily within the
limits of experimental error. The projection on the plane of the ecliptic
Table 153
Observational Data and Orbital Elements for the o-Cetid Shower
XVIII
THE DAY-TIME STREAMS
3
380
THE MAJOR METEOR SHOWERS—VI XVIII
is shown in Fig. 177. Although the inclination is high at the end of the
shower, it is low enough at the beginning to consider the possibility
that the stream might intersect the earth’s orbit again after perihelion
passage. The predicted radiant of this return shower is at a 336°,
^ —11° on July 28—a time and position coinciding with the 8-Aquarid
shower (Chap. XIV). The orbit of the 8-Aquarid stream has been
Fio. 178. Mean orbits of the 8-Aquarids and the day-time
Arietids projected on to the plane of the ecliptic.
discussed in Chapter IV. A comparison of the elements given in Table
93 (Chap. XIV) with those of the Arietids in Table 154 and of the projec¬
tion on the plane of the ecliptic in Fig. 178 shows the similarity of the
orbits. There is close agreement between the values of n. The inclination
of the 8-Aquarid orbit is 24° and the stream is 0-31 a.u. away from the
earth at its second approach on June 9. From the duration of 16 days
of the day-time Arietids the width of the stream must be at least 0*27 a.u.
There is also evidence that the 8-Aquarid stream lasts 18 days in the
southern hemisphere.f Hence, as the system of orbits is so broad.it seems
probable that the two showers are connected and are produced by one
extended meteor stream.
f McIntosh, R. A., Mon. Not. Roy. Astr. Soc. 94 (1934), 683.
Table 155
Observational Data and Orbital Elements for the ?-Perseid Stream
XVIII
THE DAY-TIME STREAMS
381
382
THE MAJOR METEOR SHOWERS—VI
XVIII
(iii) £-Perseids. The {-Perseid orbit has been computed from the
1960 and 1951 measurements. The eastward trend of the radiant and
its motion away from the ecliptic were more pronounced in 1951 , and
for that year orbits for the first and last dates have also been computed,
showing a system similar to the Arietids. The elements are given in
Table 165, and the mean orbit projected on to the plane of the ecliptic
is shown in Fig. 177.
Fio. 179. Orbits of tho (-Perseid meteor stream and an individual southern
Arietid meteor.
The inclination changes sign during the progress of the shower and
hence a portion of the £-Perseid stream must lie in the plane of the
ecliptic, giving another intersection during the winter months. The
predicted shower arising from this encounter should occur on October
11 at right ascension 28°, declination +12°. This is in the position of
the southern Arietid stream, delineated by Whipple using the Harvard
photographic technique, discussed in Chapter XV. The mean orbit
of the {-Perseid stream is drawn for comparison with Whipple’s orbit
for the southern Arietid No. 642 in Fig. 179, and there seems little
doubt that the summer day-time J-Perseid system and the autumn night¬
time S-Arietid systems must be closely related.
(iv) fi-Taurids. The /?-Taurid orbit has been computed from the 1950
and 1952 observations. The elements are given in Table 156, and the
orbit projected on to the plane of the ecliptic is shown in Fig. 177.
Whipple’8 prediction of a return of the November Taurid stream in
the summer day-time has been mentioned previously. The delineation
of the orbit of the /J-Taurid stream leaves little doubt that this stream is,
XVIII
THE DAY-TIME STREAMS
383
in fact, arising from the intersection of the November Taund orbit after
perihelion. The elements of the orbits for three of Whipple’s photo¬
graphically determined northern Taurids are given in Table 166 and
Fio. 180. Orbits of the day-timo /J-Taurid stream comparod with throe of the
orbits of the night-time Novomber northorn Taurid stream.
these three orbits are drawn in Fig. 180 together with the 0-Taurid
orbit. The relation of these orbits to that of Encke’s Comet has been
referred to in Chapter XV and will be discussed again in Chapter XXI.
XIX
THE NUMBER AND MASS DISTRIBUTION OF
THE SHOWER METEORS
The number and mass distribution of sporadic meteors and the resultant
space density was discussed in Chapter VII. From the available observa¬
tional evidence it was concluded that the relation between change of
numbers dN with magnitude m could be expressed in the form
dN = x m dm. (1)
Independent determinations of x give values lying between 2-0 and 2-7.
In terms of the mass distribution m
dN = ^,
m p
where p = 2, corresponds to the base x = 2-5 in (1). The relations
have been established by measurements on the sporadic meteor distribu¬
tion in the magnitude range from about —4 to +9. These figures give
a space density per magnitude group of about 5 0 X 10 -26 gm./c.c. and
by extrapolation a space density of about I0~ u gm./c.c. for all sporadic
meteors. Unfortunately little work has yet been done on the corre¬
sponding distributions for meteors in the major showers, the data being
limited mainly to a few visual and photographic measurements. Radio¬
echo measurements described in § 2 give hope of much more detailed
information in the near future.
1. Visual and photographic determinations of the frequency
distribution
The distribution of luminosities in the meteors of the Perseid shower
has been studied by Opikf using the double-count method described
in Chapter II. His results are summarized in Table 157. The mean value
for the base x in equation (1) is 2-5 or the same as Watson’s value for
the sporadic distribution.
The observations of the great Giacobinid shower of 1933 October 9
made by de RoyJ and by Sandig and Richter§ have been referred to in
Chapter XVI. Fig. 161 (Chap. XVI) shows the two periods during the
shower when de Roy made his naked-eye estimates of the magnitudes
t Opik, E. J., Publ. Tartu Obs. 25 (1922), no. 4.
x de Roy, F., Gazette Astronomique, 20 (1933), 170.
§ Sandig, H., and Richter, N., Astr. Nachr. 250 (1933), 170.
XIX, § 1
THE NUMBER AND MASS DISTRIBUTION
Table 157
385
Distribution of Luminosities in the Perseid Shower according to Opik
Zenithal
4 to
3-5
30
2-5
20
1-5
10
05
i 00
-0 5
-1-0
-1-5
-20
-2-5
-30
-3-5
-40
magnitude
1921
Number
%
45
10
18
4
51
21
3-5
03
25
30
85
14
5
20
73
8
■j
10
22
0-1
00
3
02
-0-5
4
025
-1-6
1
002
i
-3-5
0
0
1920
Number
30
n
85
75 ,
H
35
14
IS
2
2
1
IS
H
i
%
25
□
Q
11 |
ku
4
1
06
006
0-00
005
Efl
mM
004
••
of 534 meteors. Sandig and Richter made magnitude estimates of 101
meteors through a 70 mm. telescope. Their data have been discussed by
Watson.t The distribution of numbers observed against magnitude is
shown in Fig. 181 (a) and (6). The period II observations of de Roy (see
Magnitude
Fia. 181. (a) Nakcd-oyo magnitude distribution made during the 1933 Giaco-
binid shower by de Roy. For observing periods I and II, soo Fig. 161 (Chap.
XVI). II' is II corrected for effects of moonlight. (6) Telescopic magnitude
distribution mado during the 1933 Giacobinid shower by Sandig and Richter.
Fig. 161, Chap. XVI) were carried out in moonlight; and these have
been corrected by Watson as showm at II' in Fig. 181 (a). Watson then
applies corrections as discussed in Chapter II for the numbers missed
by the observer, and also deduces that a factor of 220 w r ould bring the
telescopic observations to the same conditions as the naked-eye observa¬
tions. The final results are given in Table 158, and the distribution of
this corrected N against magnitude is shown in Fig. 182. The slope of
this curve gives x as 2-5, in agreement with Opik’s value for the Perseid
meteors.
f Watson, F., Bull. Harv. Coll. Obs. (1934), no. 895.
3595.06 C C
386 THE NUMBER AND MASS DISTRIBUTION XIX, §1
Table 158
The Frequency Distribution Observed by de Roy and by Sandig and Richter
during the 1933 Qiacobinid Shower , as corrected by Watson
Magnitude
True naked eye
Number telescopic
220 x Telescopic
•ogio N
0
1
..
• •
0
1
8
• •
• •
0-90
2
60
• •
• •
1-78
3
223
2
(440 T)
2-35
4
433
2
440
2-64
6
1415
6
1320
314
6
• •
22
4840
3-68
7
• •
61
11220
405
8
••
91
20020
4-30
Watson compares this Giacobinid distribution with the Perseid
distribution found by Opik, and with observations of Leonid meteors
made in 1933 at Oak Ridge, Blue Hills, Hopkinton, and Wellesley. The
three distributions are compared in Fig. 183. The shape of the Leonid
curve is also substantiated by Leonid observations made by Millman.f
The Leonid and Perseid distributions show sharp kinks at about +1
mag. and +3 mag. respectively. The most rational conclusion to be
drawn from this is that these showers are lacking in faint meteors
compared with the Giacobinid shower. It will be seen that this result
is in agreement with the predictions of dispersion of small particles from
showers of great age (see Chap. XX).
Photographic measurements of the frequency distribution during
the 1946 return of the Giacobinid shower were made by Jacchia, Kopal,
t Millman, P. M., J. Roy. Astr. Soc. Can. 28 (1934), no. 3.
XIX, § 1
OF THE SHOWER METEORS
387
and Millman.f The distribution of the apparent panchromatic magni¬
tudes m p at maximum brightness for 177 meteors is given in Table 159.
Fio. 183. The Giacobinid frequoncy distribution of Fig. 182
compared with the frequency distribution for the Leonids
and Perseids.
Table 159
Distribution of Apparent Photographic Magnitudes for the 1946
Giacobinid Shower
Panchromatic
Number of
magnitude
meteors
“p
N
-8
1
-7
0
-6
4
-6
5
— 4
16
-3
33
-2
52
-1
(46)
0
(20)
The count at magnitudes —1 and 0 must be incomplete since these
magnitudes are near the threshold of the camera used. From magni¬
tudes — 2 to —6, the increase is expressed by
l°gio N = 2-50-}-0-34m p ,
leading to a value for the base x of 2-2. This is in reasonable agreement
with the value of x == 2-5 found above from the analysis of the 1933
Giacobinid shower. Jacchia, Kopal, and Millmanf also state that a
value of x = 2*5 was found in the Canadian visual observations of the
t Jacchia, L. A., Kopal, Z., and Millman, P. M., Astrophys. J. Ill (1950), 104.
388 THE NUMBER AND MASS DISTRIBUTION XIX, § 1
1946 Giacobinid shower. The authors point out that the values of m p
used above are affected by distance and by short-lived explosions on the
trail, and that a better index of the frequency distribution is given by
the integrated absolute magnitude
M p = —2-6log J I dt,
where the integral J / dt is taken as unity when m p reduced to 100 km.
distance is zero. The distribution of these integrated magnitudes is
listed in Table 160.
Table 160
Distribution of Integrated Absolute Photographic
Magnitudes for the 1946 Giacobinid Shower
Mp N
-6 3
-5 6
-4 13
-3 21
-2 61
-1 42
0 (33)
+ 1 (3)
In this case the increase is best expressed by
logioN = 2-20+0-29M p ,
giving a value of x = 1-95. This is in marked contrast to the higher
values of x found in the photographic work on the sporadic meteors. It
seems possible that the assumption of constant x over this range of
negative magnitudes is not justified. Evidently such a value could not
extend indefinitely into the brighter magnitude region.
2. Radio-echo methods for determining the frequency
distribution
It will be clear from Chapter III that the radio-echo techniques
provide a method for determining the electron line densities a 0 for
individual meteors, either by measurement of the amplitude of the
Fresnel zone patterns in cases where a 0 < 10 12 electrons/cm. path or by
measurement of the durations of the radio-echo in cases where a 0 > 10 12
electrons/cm. path. In the case of homogeneous velocity groups, as
provided by the major showers, the establishment of the distribution
of oq’s would then give the frequency distribution of magnitudes or mass
directly. Preliminary application of this idea was made by Lovell,
OF THE SHOWER METEORS
XIX, §2
389
Banwell, and Cleggf in the radio-echo measurements of the Giacobinid
shower in 1946, and LovellJ has referred to further measurements on the
1946 Geminid shower and on the 1947 Quadrantid shower. In the light
of recent developments these results cannot be regarded as reliable
since at that time it was thought that formula (6) of Chapter III
could in all cases be used to obtain the line density o^. The revised method
based on the correct formulae of Chapter III can now be employed with
confidence to determine the frequency distribution, but results are not
yet available.
An alternative radio-echo method for determining the mass distribu¬
tion has recently been devised by Kaiser and Evans.§ It can be shown||
from the theory of the evaporation of meteors that the rate of evapora¬
tion as the meteor penetrates the atmosphere is given by
n ~ 5 n
(3)
where p is the atmospheric pressure at the point in question and p mhx
the pressure at the point of maximum evaporation given by
Pmai
COS X >
1 and p m being the latent heat of evaporation and density of the meteor,
g the acceleration due to gravity, the radius and V the velocity of the
meteor before it enters the atmosphere, and \ the zenith angle. The
rate of evaporation, n mftx , at the maximum point is given by
n m*x~l(Jjfa)(\” r i,PmVc 0 Sx)> (5)
where H is the scale height, A the atomic weight, and G Avogadro’s
number.
Equation (3) can be used to plot the shape of the evaporation curve
as the meteor penetrates the atmosphere. For constant V it will also be
evident from equations (3), (4), and (5) that the extension of this curve
in height depends on and hence the mass of the meteor. If the height
distribution of the meteors in a homogeneous velocity group is deter¬
mined, the width of the distribution to half amplitude will therefore
depend on the range of meteoric masses included in the sample. It has
t Lovell, A. C. B., Banwell, C. J., and Clegg, J. A., Mon. Not. Roy. Aatr. Soc. 107
(1947), 164.
x Lovell, A. C. B., Rep. Phys. Soc. Progr. Phya. 11 (1948), 415.
§ Kaiser, T., and Evans, S., Mon. Not. Roy. As/r. Soc. 114.
|| Herlofson, N., Rep. Phya. Soc. Progr. Phya. 11 (1948), 444.
390 THE NUMBER AND MASS DISTRIBUTION XIX, § 2
been shown by Kaiser and Evans that the relation between the half
amplitude width of the height distribution Ah, and the exponent p in
equation (2) is given by
Ah
H
= 3-39(3p—?)-*.
( 6 )
So far only preliminary applications of the idea have been made to
the determination of p, using the technique of height determination
described by Clegg and Davidson, f The results indicate that the value
of p is 1 -7 for the Geminid shower, but is considerably greater for the day¬
time Anetid shower. The method has also been applied to the sporadic
distribution by selecting groups with homogeneous velocity. The various
groups all yield a value of p = 2; corresponding to the base x in equation
(1) of 2-5.
It has been a common observation in many of the radio-echo studies
that the relative increase in numbers of echoes during a major night¬
time shower show a ratio of increase over the sporadic background which
is less than the corresponding ratio found in visual observations. The
discrepancy becomes increasingly marked in radio equipment of high
sensitivity which detects meteors near the limit of naked-eye visibility,
and the effect has always been particularly prominent in the Perseid
shower. I The peculiarity has been discussed by McKinley § and by
McKinley and Millman,|| and undoubtedly arises because of the lack of
small meteors in the showers of considerable antiquity. Reference to
Fig. 183 and§ 1 also indicates that this result is well known from visual
observations in the case of the Perseid and Leonid showers. The cosmo¬
logical reasons for this disappearance of small particles in old showers
will be discussed in Chapter XX.
3. The total meteoric mass entering the earth’s atmosphere
from the shower meteors
The total daily mass and energy brought into the earth’s atmosphere
every day by the sporadic meteors has been estimated in Tables 23 and
24 of Chapter VII. By making the same assumption about the mass-
luminosity relationship it is possible to modify these tables to include
the effect of the meteors in the major showers. Although this can be
f Clegg. J. A., and Davidson, I. A., Phil. Mag. 41 (1950), 77.
X See, for example, the comments made by Prentice, J. P. M., Lovell, A. C. B., and
Banwell, C. J., Man. Not. Roy, Astr. Soc. 107 (1947), 155, concerning the radio-echo
studies of the 1946 Perseids.
§ McKinley, D. W. R., Canad. J. Phys. 29 (1951), 403.
|| McKinley, D. W. R., and Millman, P. M., Proc. Imt. Radio Engrs. 37 (1949), 364.
XIX, §3 OF THE SHOWER METEORS 391
done in detail by reference to the figures of the activity of the major
showers given in Chapters XIII to XVIH it is sufficient for the present
purpose to scale the activity from the radio-echo survey of the overall
activity shown in Fig. 184. This shows the variation of activity of the
Fio. 184. The variation of meteor activity throughout the year for day and
night periods as determined by the radio-echo technique.
sporadic background throughout the year for day and night periods,
and the peaks due to the major showers. From these curves the data of
Tables 23 or 24 (Chap. VII) can be scaled directly to give the contribu¬
tion of the showers. The data in Fig. 184 have been selected to show the
maximum sporadic activity during the day or night, whereas an average
is required for comparison with Tables 23 and 24. The ratios of shower
to sporadic activity in Fig. 184 have therefore been doubled to allow for
this. The scaling is accomplished from the ratios of the areas under the
392 THE NUMBER AND MASS DISTRIBUTION XIX, § 3
shower peaks to the average area under the sporadic background This
gives the increase per hour of the shower meteors over the sporadic
meteors averaged during the time for which the shower is active. The
daily increase in mass may be obtained by assuming that the shower
radiant is above the horizon for an average of 12 hours per day, and the
total mass brought in by the shower is then given by multiplication of
this column by the number of days for which the shower is active The
various scaling factors derived from Fig. 184 are given in Table 161. In
Table 162 the result of applying these scaling factors to the sporadic
meteor estimates in Table 23 (Chap. VU) are given for five of the most
prominent major showers. The other recurrent showers of lesser activity
such as the Ononids, Lyrids, etc., are classed together under ‘other
showers’.
Table 161
Scaltn 9 Factors far the Major Showers over the Sporadic Background
derived from Fig. 184
(The uni la are arbitrary)
Arielidt +
[•Perseida
0 Taurida
Quad rani id*
Per a eids
Oeminida
Other
ehowera
Aroa of sporadic
poak (day and
night) .
4,491
Aroa of sporadio
• •
• •
• •
• •
(avorago)
Avorago spora¬
2,245
• •
••
• •
••
• •
• •
dic por day .
31
• •
• •
• •
• «
• •
• •
Number of days
of activity
• •
16
11
2
9
A
23
Area abovo
v
sporadic back¬
ground .
194
25
63
57
142
140
61
2
Average por day
shower
Ratio--.
sporadic
••
121
39
2-2
0-7
31
10
63
2
23
7-2
The more detailed information in Table 24 (Chap. VII) can, of course,
be converted in the same manner. The information in the column headed
‘Sporadic meteors’ in Table 162 is taken directly from Table 24 (Chap.
VII). The reservations made in that chapter regarding the sporadic
mass estimates still apply to the estimates made here for the shower
meteors. There is, of course, the additional doubt as to the range of
magnitudes for which the inverse square law of mass distribution applies
in the case of the showers. The evidence presented earlier in this chapter
makes it extremely unlikely that the fainter magnitude groups still
Table 162
XIX, §3
OF THE SHOWER METEORS
393
ji*i
* ** -5
. c- «7 *> -* ^
2» — n — o b> 6
•< x >o *■» « o n
2
Is
r
1
• o t* r- e> d o
.S’""©* c< ib d> d>
X- ©*
>
■8
. o o o o o
o. Cl Cl o © CJ
-k *o — ei «*
i
» «e <* <o
!* « o — cb 6
^ — Cl cs
1
c
•••
1
1
• S ® O o « I-
J?"* — ci o ab eb
X - ci
1
* S 2 S 5 S
* 2 * • 2 5
I
• o • « ®
5 S S C £ 2
CO
!
1
1
Jf*S S S S 2
1
i§§ 1 1 1
w
J
Elfiil]
3
1‘
O
1
*5§ ? ? 8 s
^ x « - C. * 2
1
*58 S 3 5
■if E ® Cl o ©
Cl — Cl ©
i
* § 2 2 2 3
1
£
<*x
ii
CHEK
9
® ®
■? S 3 § s S
•* — ^
J
BUBB
it
1!
1
■8
n » >n — d
k r* rt O co o
■J* o d IQ C- ©
— <N
n fc
i
. *? •? — r *r
2* 2 ® 2 <£>
■* ® — « © —
d
I
S
V
K.
1
{iOO ® • ® ©
5*“* g n * -+ <d
5 5
U O
1 E
>
•8
4F 1 S 1 § S
2
o
£
k
s
.8
-i ® ® *- *©
^ d o o © ib
d — — ©
111
^ HI
wmmm
394
THE NUMBER AND MASS DISTRIBUTION XIX, §3
exist in showers such as the Perseids. Even so, within the fairly wide
range of uncertainty of these estimates, Table 162 yields information of
considerable interest. It will be seen that during the course of a year the
recurrent showers bring a meteoric mass into the earth’s atmosphere
which is only about one-third to one-quarter of that brought in by
sporadic meteors. Amongst the showers, the great Arietid and £-Perseid
day-time showers in June contribute nearly a third of the total shower
mass.
The occasional spectacular occurrences of some of the periodic showers
such as the Giacobinids are not included in Table 162; but the mass
brought into the atmosphere on these occasions must be very great. If
we consider the most recent occurrence—that of the Giacobinid shower
in October 1946—the appropriate scaling factor in Table 161 would be
about 700, and even although the shower only lasted for a few hours the
total mass would be of the order of 70 x 10 3 kg., a figure comparable with
the total mass of all recurrent showers for a whole year.
4. The total mass and density of meteoric particles in the
orbits of the major showers
From the mass estimates of the previous section it is possible to
speculate on the total mass and density of the meteoric material in the
orbits of the major showers, on the assumption that the density is
uniform around the orbit. This latter assumption is fully justified for
the recurrent showers listed in Table 162. From the data about the
various shower orbits given in the previous chapters it is possible to
calculate the linear length of the various orbits. Also from i and to
and the number of days for which the shower is active, the cross-section
of the stream can be found. Hence the total volume containing the
meteoric particles in the entire orbit can be calculated. The number of
meteors swept up by the earth in time t are those contained in a cylinder
of volume ..
where r t is the radius of the earth’s atmosphere (6,400 km.) and v the
relative velocity of the earth and the meteors. Hence by putting t = 1
hour or 1 day and using the appropriate mass swept up for the individual
showers in Table 162, the density in the orbit can be calculated. For v,
the geocentric velocity of the particular shower meteors has been used.
The data calculated for the showers discussed earlier in this chapter are
given in Table 163.
As expected, the densities in the orbit are somewhat higher than for
the sporadic meteors, being of the order of 10 -23 to 1O -24 gm./c.c. compared
OF THE SHOWER METEORS
XIX, §4
395
with 10“ 24 to 10" 25 gm./c.c. for the sporadic distribution. The total mass
in each orbit is about 10 12 kg. (10 9 tons).
Table 163
The Density and Total Mass in the Orbits of the Major Showers
Ariftidi
{-Perseidt
B-Taurid*
Quadranlidt
Peneidt
Geminidt
(1) Circumference of orbit
(km.) .
0-4X10*
12 6x10*
15 0x10*
17-2x10*
67-3x10*
0 7 x 10'
(2) Width of active region
(km.) .
3 0x10’
3 5x10'
1-5 x 10’
0 5 x 10’
2-1 x 10 ’
1-5x10’
(3) Total volume around
orbit (km.)* .
118x10**
12-4 x 10'*
2 0 x 10“
0 3 x 10“
23-7 x 10”
1-7x10”
(4) Volume containing
meteors swept up in
one day (km.)*
4-3 x 10“
3 2 x 10“
3-4 x 10“
4-4x10“
6 6x10“
4-0x10“
(5) Density in orbit
(kg./km.*)
6 0 x 10 -'*
1-4x10-“
15 1 x 10"“
2-4 x 10-“
12 0x10““
(0) Total mass (kg.)
7-2:
<10“
0 4 x 10“
0 5x 10“
5-7 x 10“
2 0x10“
NoUt. (1) Calculated from major and minor axes of orbits.
(2) Calculated from number of day* of duration of shower and I and w of the orbit.
(3) From (1) and (2).
(4) From *rrj tv with r, - radius of atmosphere (6,400 km.), t - one day and v - geo¬
centric velocity of shower meteors.
(5) From (4) and mass per day in Tabic 162.
(6) From (4) and (5).
For comparison with these figures it is possible to speculate on the
mass of meteor debris associated with a new periodic shower such as the
Giacobinids. In the previous section it was estimated that during
the few hours of activity of the shower about 7 x 10 4 kg. of debris entered
the atmosphere. From line 4 of Table 163 it can be estimated that this
debris must be contained within a volume of about 2x 10 13 km. 3 Thus
the density of matter in the active region is about 3 X 10“® kg./km. 3 , or
a thousand times higher than the density calculated for the recurrent
showers. The meteors are very localized in the orbit and from Chapter
XVI it can be estimated that they are unlikely to extend for more than
about 100 days around the orbit or, say, 10® km. Since the earth sweeps
through the active part of the stream in about 2 hours the cross-section
is around 10 10 km. 2 Thus the total volume containing the debris is only
about 10 18 /km. 3 , and the total meteor mass about 10 9 or 10 10 kg. Even
allowing for large factors of uncertainty this mass is 100 to 1,000 times
less than the total mass in the recurrent streams of Table 163. Of course,
in this estimate the mass of material in the comet itself which is still
an entity in the case of the Giacobinid shower has not been included.
The significance of these mass and density estimates will be discussed
in Chapter XXI.
396
THE NUMBER AND MASS DISTRIBUTION XIX, §4
It is also interesting to notice that the individual particles are widely
scattered in space even in the most concentrated showers. Reference
to Table 24 of Chapter VII shows that in the sporadic background a
body of mass 1 mgm. occurs on the average in 10 23 c.c. (~ 10 7 cu. miles)
of space, and one of mass 1 gm. in about 10 28 c.c. (~ 10 10 cu. miles) of space.
Even in a most concentrated display like the Giacobinid shower the
corresponding estimates only rise to 10 19 c.c. (~ 10 3 cu. miles) for a body
a mass 1 mgm. and 10 22 c.c. 10® cu. miles) for a body of mass 1 gm.
XX
THE DISPERSIVE EFFECTS IN METEOR
STREAMS
The discussions in previous chapters of this book have indicated that
most of the meteoric matter in the solar system is widely dispersed.
Perhaps one-quarter or one-fifth of the total is, however, associated with
the major showers—debris moving in specific orbits, or closely related
orbits, in many cases dispersed uniformly around the orbit. There are
various effects capable of dispersing meteoric debris. As regards the
shower meteors it seems natural to assume that the debris originally
existed in one conglomerate—such as a comet—and that these disper¬
sive forces have scattered the debris in the course of time around and
about the orbit. On this view the periodic streams, such as the Giaco-
binids, where the debris is still localized, are comparatively young and are
still in the initial processes of dispersion, whereas the recurrent streams
such as the Perseids where the debris is uniformly scattered around the
orbit, are of great age. There is a good deal of circumstantial evidence
in support of this general view, and the main idea of dispersion is not
now seriously questioned.
A further extrapolation of this idea leads to the view that the sporadic
meteor content of the solar system is the result of the ultimate dispersive
effects on matter which was originally closely conglomerated. On this
question, however, there is not yet good evidence or agreement, since
this sporadic matter might equally well be primeval. A solution of this
particular problem would evidently be of great importance as regards
the origin of the solar system, and the more detailed investigation of the
individual orbits of sporadic meteors which may be expected during the
next few years may provide the basic data for the investigation.
The present chapter is mainly concerned with the forces which disperse
the debris in the orbits of the major showers, and with the possibilities
of estimating the age of the showers from the extent of the dispersion.
1. The effect of planetary perturbations
It is easy to show that the main disturbances are caused by Jupiter
and Saturn. If the attractive force of Jupiter on a body at unit distance
is represented by 1,000, then the appropriate values for other members
of the solar system at unit distance are Sun 10 6 ), Saturn (300),
398
THE DISPERSIVE EFFECTS XX, §1
Neptune (54), Uranus (46), Earth (3-2), Venus (2-6), Mars (0-34), Mercury
(0-15). Thus, except in the case of a very close approach to the smaller
planets, the main perturbations are always due to Jupiter or Saturn.
The main effect is to accelerate the motion of the body along the line,
body-planet. The composition of this acceleration with that along the
line, body-sun, may give rise to various changes in the orbit. The exact
calculation of the perturbations, which is described in the standard
texts, is a complex procedure. The following simplified treatment which
illustrates the particular problem under discussion here is due to Porter, t
The standard equations of motion including the effect of an attracting
body of mass m 1 (x I , y„ z,) at distance p from the body are of the form
( 1 )
where k 2 is written as the gravitational constant (see Chap. V). This is
with reference to the centre of mass of the whole system. Alternatively
in heliocentric coordinates with r and t x the radii vectores of the body
and planet
(2)
Equation (2) with the corresponding ones in y and z can be used to com¬
pute the perturbations of the body as described in the standard texts.
Alternatively (2) can be written in the form
g+k*+»£-»". (3)
where m 1 R is the perturbative function. Except where great accuracy
is required it is convenient to determine the variations in the elements
as distinct from the coordinates. In this case a simplification results
by taking a new set of axes in the plane of the orbit and moving with the
body. The X axis is along the line body-sun; the Y axis in the plane of the
orbit, 90° in front of the body, and the Z axis perpendicular to the orbit
plane. The coordinates of the body are then r, 0,0. From equation (2), S,
T , and W are computed, and are regarded as the attractive forces along
the axes defined above. Then from the equations in Chapter V the
following relations for variations of the elements are obtained, where
t is the interval in days. In these equations q> is the angle of eccentricity
f Porter, J. G., Comtla and Meteor Streams, Chapman & Hall, 1962.
XX, §1
IN METEOR STREAMS
399
(e = sinq>), and E the eccentric anomaly, otherwise the notation is the
same as in Chapter V.
= rsinfai+iOcoseci W
at
= rcos(a >+v)W
= acos<psini»5-f acos<p(cosE+cosv)T
at
-? c ° 8 vS+2±- r,in, .r+2s in «i i ^
41 =
t w = (P cos V cot<p - 2r cos<p)5- cot<p sin , (p+r) T
e
^(esin.S+Pr)
(4)
B
The qualitative effects of the perturbations may readily be seen from
equations (4). The orthogonal component W, always due, in practice,
to the major planets, will be negative as the body moves forward from
the ascending node (as increases from 0 to 180°), and will be positive
in the remaining part of the orbit. Thus the change in node given by
dft/dt in (4) will always be negative. Hence the effect of a planetary
perturbation on a body is always to cause the node of the orbit to retro¬
gress if the motion is direct, and to advance if the motion is retrograde.
This is a common effect and its importance for the case of meteor streams
is evident from previous chapters of the book. The main effects of the
perturbations given by equations (4) may be summarized by reference
to Fig. 185.
400 THE DISPERSIVE EFFECTS XX, § 1
(а) Node: affected by W only, which changes sign at ft. Thus the
node retrogresses for direct motion.
(б) Inclination: affected only by W. Maximum positive value at SI
and maximum negative value at .
(c) Major axis: attraction -\-T always increases major axis. -\-S has
no effect at perihelion and aphelion, but increases the major axis
in the region PC A and decreases it in the second half ABP.
(d) Line of apsides: +S causes PA to move forward when the body is
in the region CAB and backwards in the region BPC. -f T causes
forward movement of PA when the body is in the region PCA, and
backward in the region ABP.
(e) Eccentricity: -f S increases e during path PCA and decreases e
during path ABP. -f-T has maximum positive effect at P and
maximum negative effect at A. The effect is zero at the two points
where r = b.
Equations (4) give the rate of change of the elements with time and the
total effect has to be obtained by integration. There are various methods
of performing these calculations which are described in the standard
texts. The final effect depends not only on the closeness of approach to
the planet but also on the duration of the attraction, and is therefore
greatly dependent on the nature of the orbit. In particular, particles
moving in orbits of high inclinations can only suffer severe perturbations
when a close approach to a planet occurs at the node. Undoubtedly this
fact accounts for the stability of such meteor streams as the Perseids
and Lyrids which are of great antiquity. On the contrary the striking
effect of perturbations by Jupiter on an orbit of short period and low
inclination is well evidenced by the case of the Pons-Winnecke meteor
stream. The changes in the elements of this orbit between 1858 and 1945
have been listed in Table 147 of Chapter XVII. During this time the
perihelion point moved from inside, to outside the earth’s orbit, and the
orbit itself has become larger and more circular, with greater inclination.
The distance of nearest approach to the earth's orbit has now increased
so much that a further occurrence of the Pons-Winnecke meteor shower
appears very unlikely.
Even when the conditions are not such as to give rise to these extreme
effects, the changing position of the node caused by the orthogonal
component W must always be present—a point which formed the basis
of the identification of the Leonid orbit with comet 1866 I as described
in Chapter XVI. Further, the collective perturbations which arise from
XX, §1
IN METEOR STREAMS
401
many revolutions of the particles around the sun will eventually cause a
conglomerate to disperse around the orbit—each individual particle
following its own orbit within the main stream and suffering perturba¬
tions different from its neighbour. Hence, although the perturbative
effects may not be violent enough to swing the entire orbit away from the
earth as in the case of Pons-Winnecke, even in the most favourably placed
orbits such as the Perseids there will be a constantly changing position
of the node and an eventual dispersion of the particles around and about
the orbit.
2. The ejection of meteoric material from comets
Although there is general acceptance of the fact that many of the major
meteor showers are moving in comctary orbits, the idea that they arise
from the partial or complete disintegration of the comet is by no means
universally accepted. Nevertheless, there are now powerful reasons for
the belief, and in this case the mode of ejection of the meteoric material
would be a prominent factor in the dispersal of the material. The idea
that meteor streams are formed by the ejection of material from comets
appears first in 1877 in the work of Bredikhine. The most recent develop¬
ments of the idea due to Whipplef will be referred to in Chapter XXI.
Whipple shows on the basis of the cometary model that the meteoric
particles will be ejected from the comet at an appreciable rate when it
is within about 2 a.u. of the sun, and that the velocity of ejection Au
will be given by
Au = (rr) i ^ m/sec - (6)
where r c is the radius of the comet in km., 1 /L is the heat absorption
coefficient, r is the radius of the meteoric particle in cm., and q the peri¬
helion distance of the comet in a.u. Evidently the variation in ejection
velocity with r and q will be a prominent effect in the dispersion of the
meteoric particles. The particular case of the Perseid stream has been
studied by Hamid.J For r c = 5 kin., r = 01 cm., L = 2, q = 1 a.u.
the velocity of ejection given by (5) is 16-5 m./sec. The ejection will be
in all directions with a preference in the direction of the sun. The change
in the angular orbital elements due to the ejection velocity < 0°-l, but
the change in the period is shown to be appreciable. Hence after only a
few dozen revolutions in the orbit the ejected meteoric material will be
distributed along the entire orbit.
f Whipple, F. L., Astrophys. ./. Ill (1950), 375; 113 (1951), 464.
t Hamid, S., Harvard (doctoral dissertation), 1950.
D d
3595.66
402 THE DISPERSIVE EFFECTS XX, §2
This mechanism of ejection can therefore give rise to a distribution
of the meteors around the orbit, but since the effect on the angular ele¬
ments is small, the cross-section of the stream will not be greatly increased.
The widening of the stream will occur through the effects of the succeed¬
ing planetary perturbations discussed in § 1. Hamid shows that the
observed dispersion of the photographic radiants of the Perseid meteors
can be adequately explained on this basis if the shower has endured for
about 200 revolutions of the parent comet.
3. The Poynting-Robertson effect
In 1903 Poyntingf considered the effects on the motion of a small
body in the solar system when it absorbed and subsequently re-emitted
solar radiation. He concluded that there would be a tangential drag,
which would decrease the angular momentum of the body and eventually
cause it to fall into the sun. It is now generally recognized that this
effect exists and that it is of great importance in meteor astronomy, but
the correct explanation of the drag was not given until 1937. Poynting
attributed the drag to a back pressure of radiation tending to retard the
motion of the emitting body ; he conceived this as due to a crowding-up
of radiation in front of the particle and to a corresponding thinning-out
behind. His value for the magnitude of this force was $0V/c 2 , where 0
is the rate at which the particle is radiating energy, V its velocity through
space, and c the velocity of light. The gravitational force varies as the
cube of the linear dimensions of the body whereas 0 depends on the
square of the linear dimensions. Thus the drag should become increas¬
ingly marked as the size of the body decreases. Poynting estimated
that a body of radius 1 cm. and density 5-5 at the earth’s distance from
the sun and with the earth’s velocity could make 10 8 revolutions before
falling into the sun, whereas a body of radius lO" 3 cm. would only make
10 5 revolutions.
The next contribution to the subject was made by LarmorJ in 1913,
who gave an alternative treatment on classical electromagnetic theory
of the retarding force on a body moving with velocity V arising from its
own radiation. Larmor’s value for the force was ©V/c 2 — three times
that obtained by Poynting. It was pointed out,§ however, that the
braking effect of such a force was in contradiction with relativity theory,
f Poynting. J. H., Phil. Trans. Roy. Soc. A 202 (1903), 525; Collected Scientific Papers,
Art. 20 (Cambridge, 1920), 304.
X Lnrmor, J., Proc. 5th Internal. Congress Mathematics, 1 (Cambridge, 1913), 197.
f Observatory, 40 (1917), 278.
XX, §3
IN METEOR STREAMS
and in a detailed investigation Pagef showed that a moving body does
not suffer retardation as a consequence of its own radiation alone.
Subsequently Larmorf admitted the correctness of this result and
agreed that an isolated body cooling in space would not be retarded,
since the back thrust of the radiation would be compensated by the
increase of velocity resulting from the conservation of momentum as
the mass decreased. But he then pointed out the true cause of the
Poynting drag and resolved the paradox . for Poynting’s particle
describing a planetary orbit the radiation from the sun comes in, which
restores the energy lost by radiation from the particle, and so establishes
again the retarding force — OV/c 2
The original misconception about the existence of this force arose
because of the use of a stationary frame referred to the particle, in which
case the process of absorption and re-emission does not introduce any
net force. On the other hand when the particle is considered in the solar
reference frame there is a force proportional to the velocity of the
particle.§ The force is clearly of very great interest in meteor astronomy
since it leads to a separation of the meteoric particles according to their
size, an effect which, as will be shown, is very marked in periods of time
which are astronomically small.
The full relativistic treatment of the effect was given by Robertson||
in 1937, and his results arc now generally accepted. The simplified
Newtonian approximations, involving only first order terms in V/c, are
sufficiently exact for use in the general meteor problems considered here.
In this case the equations of motion for the particle are expressed in
terms of the two vectors
v -% <•>
where n is the unit vector in the direction of the incident beam. Robert¬
son’s equations of motion for the particle then become
t Page, L., Phys. Rev. 11 (1918), 376; 12 (1918), 371.
J Larraor, J., Poynting'8 Collected Scientific Papers (Cambridge, 1920), p. 757.
§ In terms of quantum theory, the quanta emitted by tho sun carry a purely radial
momentum and hence, when absorbed by a particle moving in tho solar system, will
produce a tangential dragging force in addition to normal radiation pressure. Since
the re-radiated quanta are isotropic with respect to the particle there is no recoil effect
duo to its own radiation.
|| Robertson, H. P., Mon. Not. Roy. Astr. Soc. 97 (1937), 423.
404
THE DISPERSIVE EFFECTS
XX, |3
where V a is the component of the velocity V in the direction n. The
first term is due directly to the radiation pressure in the direction of the
beam, weakened by the Doppler factor (1 — (VJc)). The tangential drag
is given by the second term.t
For a particle moving in the solar system n is the unit vector along
the radius vector from the sun, and the energy density, d, will fall off
inversely as the square of the distance from the sun. If 6 is the earth-sun
distance, and E the solar constant (E = 1-35 x 10« ergs/sec./cm. 2 ) then
at distance r from the sun
d = — f — m * c
cr 2 * r 2
where - - A ^* _ 356* 2-51X10“ ' (8)
me 2 4rpc 2 pr
In the second expression for k the cross-section A and mass m of the
particle are given in terms of a sphere of density p and radius r, large
compared with the wave-length of the incident radiation.
Adding to equation (7) the gravitational force Y (Mm/r 2 ) in the
direction —n, the equations of motion in polar coordinates (r,0) in the
plane of the orbit with the sun as pole are given by
— — 2 * dr
dt 2 \dt) r 2 r 2 dt’ (9)
1 d_/ 2 d0\ _ _ k d0
r dt\ dt) ~ r dt’
( 10 )
where p. = n 0 —*c i®solar gravitational constant, |x 0 (= yM), reduced
by kc as representing the repulsive effect of the direct radiation pressure.
Equation (10) integrates to give
»= 4 ® -
(ii)
where H is the instantaneous value of the angular momentum and h
the initial value.
From these equations Robertson calculated the secular perturbations
f The interpretation of the effect in terms of classical notions is clear from equation
(7). The particle absorbs energy at the rate cf = c. Ad. This is re-radiated isotropically
about the particle which is moving with velocity V and therefore carries away electro¬
magnetic momentum at the rate (cf/c*)F. Since mechanical and electromagnetic
momentum is conserved this process must cause the particle to lose momentum at the
rate fP/c which therefore appears as the retarding force given by the last term in
equation (7).
XX, § 3
IN METEOR STREAMS
405
for an osculating ellipse of semi-major axis a and eccentricity e as follows :
da *(2-f3e 2 )
dt “ “a(l—e 2 )*’
de 5/ce
dt — 2a 2 (l—e 2 )**
( 12 )
(13)
For the advance of perihelion Robereton obtained
dw_ 3y*Af*jI
dt c*a*(l—e 2 ) ’
(14)
The most striking consequence of this retardation is that any particle
moving in the solar system will eventually be swept into the sun;f in
fact it follows from (11) that a particle cannot survive for 11/2™ revolu¬
tions about the sun. (The case mentioned earlier, considered by Poynting,
of a particle of radius 1 cm., p = 5-5 in a circular orbit at the earth’s
distance would survive 1-55X 10 8 revolutions—in close agreement with
Poynting’s value of 10® revolutions.)
The time scale, and other consequences of this retardation for particles
of meteoric size have been considered in detail by Wyatt and Whipple. J
As far as n is concerned, drr/dt in (14) is only significant for large and
dense bodies where jl ~ yAf; and the change is insignificant for meteoric
particles (in the case of Mercury, for example, the change amounts to
only 43" per century). For small particles the changes in e and a are of
most interest. For an initially circular orbit (12) integrates to give
the total time of fall into the sun as
a 2
t = — = 7-Ox 10 8 rpa 2 years, (15)
where the radius r is in cm., density p in gm./c.c., and the initial distance
a in astronomical units. For an eccentric orbit (12) and (13) give the
relation between a and e, which on integration gives
a =
Cc 4 ' 5
1 — e 2 ’
(16)
The constant C in (16) can be computed, given a 0 and e 0 at any arbitrary
fcime C = a 0 e 0 -*«(1—e*). (17)
From (16) and (13) a relation may be obtained involving only e and t
de 5*(1—e 2 ) 3 ' 2
dt “ 2C 2 e 3/5 ’
(18)
t Unless, of course, tho radiation pressure balances the gravitational attraction—
this critical limit being given by rp > 6*72 x 10“ s gm./cm.*
X Wyatt, S. P., and Whipple, F. L., Aslrophys. J. Ill (1950), 134.
406
THE DISPERSIVE EFFECTS
XX, §3
Hence (for e 0 > e)
s/
e 0 0
(19)
where r and p are in c.g.s. units. C 2 with dimensions (a.u.) 2 is obtained
from (17) by using the constants of the orbit. The integral cannot be
found directly, but the integrand is independent of the particle, and
numerical integrations suffice for all cases. Wyatt and Whipple cal¬
culated values of the function
e
for various values of e as given in Table 164. Substitution of r, p, and C 2
then gives the total time for the particle to spiral into the sun.
Table 164
Data for Calculation of Time of Fall of a Particle into the Sun as a Result
of the Poynting-Robertson Effect
0
G(e 0 )
(t-to)
10’rpq* ^
m
GK)
lOVpq* ^
000
• •
0-704
0-78
0-771
4-10
005
0 0052
0-778
0-846
4-42
010
00158
0-858
081
0-889
4-60
015
00305
0946
0-82
0-934
4-79
020
0 0480
1 04
083
0-983
5-00
0-25
00710
115
0-84
104
5-23
0-30
00969
1-27
0-85
110
6-49
0-35
1-40
0-86
116
6-77
0-40
1*55
0-87
1-23
6-08
0-45
1-72
0-88
1-32
6 43
0-50
1-92
0-89
1-41
6-83
0-55
0-305
2-15
0-90
1 51
7-29
0-60
0-370
2-42
0-91
1-63
7-82
0-62
0-400
2-54
0-92
1-78
8-45
0-64
0-432
2-68
093
1*96
9-22
0-468
2-82
0-94
2-17
10-17
068
2-98
0-95
2-45
11-39
0-70
0 548
3-16
0-96
2-82
13-06
0-72
0-595
3-36
0-97
3-37
16-50
0-74
0-647
3-57
0-98
4-30
19-60
0-76
0-705
3-82
0-99
6-37
28-89
Wyatt and Whipple simplified the calculations further for the total
time of fall by writing (16) as
C 2 = q 2 (l-fe) 2 e- 8 / 6 (21)
[where q = a( 1 —e)].
XX, §3
Then (19) becomes
IN METEOR STREAMS
407
Jl-13(l+e 0 ) 2 f* e 3/6 de
(fc—to) years = 10’rpq 2 -^- J
ft
( 22 )
The quantity
1*13(1+e 0 ) 2 f e^de
ej /6 J (1—e 2 )^ 2
e
is also tabulated in Table 164,
and from this the total time of fall into the sun of a particle of radius r
and density p can be readily obtained by substitution of the perihelion
Fio. 186. The changes in semi-major axis a, and porihelion
distance q as a function of time due to the Poynting-
Robertson effect. Subscript L refers to the Leonid orbit and
G to the Giacobinid orbit.
distance q in a.u. For the calculation of the time required for the
particle to change between two arbitrary eccentricities, it is, of course,
necessary to compute by using G(e 0 ).
The change of the semi-major axis a and the perihelion distance
q with time for particles in the present Giacobinid and Leonid orbits
have been calculated by Wyatt and Whipple and are shown in Fig. 186.
The decrease in a is fairly linear; that in q very slow until the final
408
XX, §3
THE DISPERSIVE EFFECTS
stages. The calculations for the total time of fall into the sun of the
particles in some of the major showers are given in Table 165. Whipple’s
photographic elements (Chap. XV) have been taken for the orbit of the
Cemimd meteors, and Yamamoto’st elements for the orbits of the
presumed parent comets for the remaining showers. These associations
ugree with the conclusions of Chapters XIII to XVII with the exception
of the doubtful Orionid-Halley Comet relationship. The total time of
fall computed from the data of Table 164 is given in column 6 For
cSldfrom ^ 7 6iVeS the COrreSP ° nding UmeS f ° r a Circular ° rbit
Table 165
Times of Fall into the Sun of Meteoric Particles in the Major Shower Orbits
Shower
*“■ a mm
Parent
comet
a
e
C
(t-t.)
To’rp
. .
!■§-if -Si ,
ill ill ft
JHiaoojaij
T
Encke
1852 in
1933 III
Halley ?
1868 I
1862 III
1861 I
1- 396
2- 210
3 5259
3-520
17-96
10325
24 277
55 665
0 900
0-8498
0-75592
0-7160
09673
090542
0-96035
098346
0289
06995
1- 8902
2- 241
1186
2-0145
1-9491
1-8508
0-143
0 605
2- 79
3- 32
6-10
7-24
12-2
186
1-4
3-4
8-7
8-7
230
75
410
2200
It is evident from these results that the lifetime of small meteorio
bodies in the solar system is short, astronomically. For example a
particle of radius 0 05 cm. and density 4 gm./cm.*, corresponding'to
about a fifth magnitude meteor moving in the orbit of Halley’s Comet
would be drawn into the sun in about 10,000,000 years.
A further factor of extreme interest in meteor astronomy is the
possibility of observing the Poynting-Robertson effect in the major
showers by virtue of the selective effect arising from differing particle
size and density—the smaller ones being drawn towards the sun much
faster than the larger ones. Wyatt and Whipple estimated the order of
times required to separate meteors of magnitude +5 and —2 so that the
earth would pass from one limit to the other in 5 days. In order to do
this the showers in Table 165 with inclinations less than 40° were con¬
sidered, and their inclinations assumed to be zero. The perihelion
advance was neglected and the earth’s orbit taken as circular. The
density of the meteors in each shower was taken as 4 gm./cm. s and the
t Yamamoto. A. S., Pub.'Kuxuan Obs. 1 (1936), no. 4.
XXi 53 IN METEOR STREAMS
radii calculated from the luminosity-mass relationships discussed in
Chapters VII and XIX. The estimates are given in Table 166.
Table 166
Times of Separation of Meteors of Magnitude —2 and +5 due to
Poynting- Robertson Effect
Shower
Gemini ds
Taurids
Giacobinids
Bielids
Leonids
Orionids ?
Time (years)
7 X 10 4
5X10*
1X10*
2 x10*
3x 10*
5X10*
Wyatt and Whipple state that such a separation effect has not been
observed. However, in the case of the Geminid shower the radio-echo
data listed in Chapter XV show that there is, in fact, a very marked
separation of particle sizes. The most active region of the shower is near
the end and consists of a marked concentration of heavier particles
compared with the earlier activity of the shower. In other words the
dispersion is exactly of the type to be expected from the operation of the
Poynting-Robcrtson effect over a period of some 10* years. It is well
known that the Perseid shower contains mainly large particles, and in
this case it seems likely that the smaller content has been sifted away from
the original orbit by the Poynting-Robertson effect. The high inclina¬
tion of the orbit provides a ready explanation why theso smaller
particles moving in an orbit of reduced major axis arc no longer inter¬
cepted by the earth. As regards the other showers listed in Table 166,
sufficient radio-echo data are available only for the Giacobinid shower.
No separation is found, a result to be expected in view of the showers’
recent origin. In thecaseoftk day-time showers, which are intercepted
on the sunlit side of the eart\', it is clear that the Poynting-Robertson
effect will act to produce the heavy particles at the beginning of the
shower. An inspection of the radio-echo data has not revealed any
separation in particle sizes with time, which may indicate that the day¬
time streams have an origin more recent than the time scale of Table
166. The perturbative effects discussed earlier in this chapter are non-
selective as regards particle sizes; moreover, the showers of low inclina¬
tion considered in Table 166 are those most susceptible to planetary
perturbations. Hence the showers may have been dispersed in a non-
selective manner within the time scale of Table 166; thus, in cases where
the Poynting-Robertson effect is not observed, the times in Table 166
can only be regarded as an upper limit to the age of the shower.
410
XX, §4
THE DISPERSIVE EFFECTS
4. The Yarkovsky effect
According to (jpik.t Yarkovsky published a pamphlet in St. Peters-
burg about 1 900 dealing with the effect of radiation pressure on a rotating
particle. The effect arises on account of the excess of radiation emitted
tw eVeni " g ,' hemis P here over the ‘morning’ hemisphere. It appears
• , f V6r ^ s g 1 excess °f the evening over the morning temperature
effect ml! 106 ♦ ^ ° f thC Same ° rder M the p oynting-Robertson
Yarkov!! V , and ° rbital m0ti ° n are in the same dire °tion the
rotatnn 13 ° PP ° Site 40 the p oynting-Robertson effect; if the
Ration,' opposite to the orbital motion the two effects work in the same
the Y " tak? w * - **■«■*-
y = __C 2 A T
U 3 T
■ cos 0,
(23)
enCe 8UrfaCe radiative tem P era tures between
the evening and monung pomts at equinox, and 0 the inclination of the
equator of rotation to the plane of the orbit.
(in F S eco a nds i ny m SPhere in ^ With peri ° d of axial rotation *
(m seconds), moving m an orbit with semi-major axis a (a.u.) Opik gives
^ T = de g. absolute ( 24 )
taking into account appropriate values for the conductivity, specific
heat, and solar constant. Equation (24) remains valid provided the
daily temperature oscillations die out .ell outside the centre of the
particle, that is provided r
'>1™* (25)
where r is the radius of the particle.
Otherwise if r < j
then (approximately)
Substitution in (23) gives
AT = --L.
6 a*
y/Pg = -3-97 cos
a
(26)
(27)
(28)
.olf^pht; -T^Zio’ry X, 5 * (,95,, • I65 ' '° Pik 8ta,eS th8t his
XX, §4
IN METEOR STREAMS
411
and
y/P = -19-8 COS 0- 2
(29)
corresponding respectively to (24) and (27).
Forretrograde motion (180° > 0 > 90 °) y works in the same direction
as P., leading to an accelerated rate of decrease of the major axis. For
direct motion (0° < 0 < 90°) the effects are opposite and da/dt is
decreased or even inverted so that the particle spirals away from the
sun. For given XV or r the ratio depends on a—and for a certain value a 0
the ratio is — 1, and the two effects will cancel.
In applying the idea to meteor particles Opik draws attention to his
estimatesf that for an age of 3x 10 * years these particles will possess
an average period of rotation as a result of collisions with smaller dust
particles of _ ....
W = ——sec. ( 3 °)
1800
for 0 01 < r < 5 cm., and of
W =
r
18000
sec.
for r < 0 01 cm.
Even if these periods arc underestimated by a factor of 10 (which
would be the case if the age or frequency of Collisions were overestimated),
it is clear that the cases represented by (24), (25), and (28) will be
predominant. Thus from (28)
y/p g = —0-3 cos 0 r* /4 /a for r > 0 01
and y/Pg = — 0*09cos© r 1 ' 2 /a for r < 0 - 01 .
Putting cos© = J the ‘equilibrium’ conditions (y/P K = — 1) 1)6
attained in the following cases
r (cm.) 10“ 3 10- 2 10- 1 1 3 If
a 0 (a.u.) /0-002) (0 006) (0 04) 0-2 0-5 1-1
A solid particle is unlik/v to exist at a distance closer than 0 01 a.u. to
the sun, thus the equilibrium distances a 0 are only likely to have signifi¬
cance for large particles r = 1 to 10 cm. The Yarkovsky effect is thus
probably negligible for meteoric particles, except for those of large size
in the fireball class.
5. Conclusion
The summary of possible dispersive effects in this chapter leads to the
impression that planetary perturbations, coupled with the possibility
t Opik, E. J., Pub. Tartu Ob*. 28 (1936), no. 6.
412
THE DISPERSIVE EFFECTS
XX, §5
of differential ejection velocities from the original conglomerate, are the
main influences dispersing meteoric debris around the orbit. The
Poynting-Robertson effect introduces a selective drag which in the
course of time will separate out the particles in a shower according to
their size, eventually causing all to fall into the sun—the small ones
faster than the large ones. The Yarkovsky effect would not seem to be
an important dispersive influence except possibly for the larger meteoric
bodies in which case it might either aid or hinder the Poynting-Robertson
drift, depending on whether the motion in the orbit is retrograde or direct.
The possibility of other dispersive influences has been mentioned by
Whipple.f Meteors must carry a positive charge, as a result of photo¬
electric effects due to the sun’s radiation, and if the sun has a magnetic
field a motion of the line apsides must result^-greater for smaller meteors
than for large ones. Simple electrostatic effects might also tend to
disrupt an originally compact stream. No detailed calculations have yet
been made on these topics but their magnitude hardly seems likely to
be a greater selective influence than the Poynting-Robertson effect
within the time scale of the major showers.
t Whipple, F. L., Proc. Amtr. PhU. Soc. 83 (1940), 711; 91 (1947), 189.
XXI
COSMOLOGICAL RELATIONSHIPS OF
METEORS
1. The association of the major showers with comets
The extent of the relation of major showers with comets has been dis¬
cussed in earlier chapters of the book. Mainly as a result of the work of
Schiaparelli, it was realized in 1866 that the orbit of the Perseid shower
was closely related to that of Comet 1862 III, and the orbit of the
Leonid shower with that of Comet 1866 I. Subsequently, other close
associations were recognized, and Table 167 summarizes the possible
cometary-meteor stream associations known at the present time.
Table 167
Cometary-Meteor Stream Associations
Meteor shower
Comet
Date
Radiant
Clotett approach
of comelary orbit
( Comet-Earth )
Remarks
Quadrantida .
(T)KozUc*
Peltior
1939a
Jan. 3
a 5
230 +60
a.u.
• •
Doubtful
Lyrida .
1861 I
April 21
271 +34
-0 002
••
Jq-Aquarida'l
\ Orionida J
0-Taurida (day-timo)
Taurida .
{•Poraoida (day-timo)
S-Ariotida
(t)Halloy
Encke
/May 6
\Oct. 20
Juno 30
Nov. 10
Juno 10
Oct. 20
336 -1
95 +16
90 +20
66 +20
60 +22
41 +10
J -0 064
• •
• •
• •
• •
Doubtful
Common orbita
originally. Now
aeparatod due
to porturba-
tiona (aeo text)
Pona-Winnocko
Pona-
Wiunecko
Juno 30
208 +64
-0042
• •
Pereoida .
1862 III
Aug. 11
45 +58
+ 0010
• •
Giacobiuida
Giacobini-
Zinner
Oct. 10
262 +54
+ 0004
• •
Leonids .
1866 I
Nov. 15
151 +23
-0052
• •
Bielida .
Biela
Nov. 30
23 +44
-0018
Ursida
Tuttlo
1939 k
Dec. 22
200 +80
+ 0100
• •
There are four main criteria by which the identity of the orbits of the
comet and the meteor stream must be judged, (i) Similarity of orbits,
provided the comet makes a sufficiently close approach to the earth.
414
COSMOLOGICAL RELATIONSHIPS
XXI, § 1
(ii) Recurrence of the shower in a period compatible with that of the
comet, (iii) Regression or advance of the date of the shower, correspond¬
ing to the movement of the node of the comet, (iv) Daily movement of
the radiant in the case of a long enduring stream. Of the possible associa¬
tions listed in Table 167 only six would receive universal recognition on
this basis as undisputed cases of the relation of a meteor stream and a
comet (Lyrids, Pons-Winnecke, Perseids, Giacobinids, Leonids, and
Bielids), and two of these are now lost streams (Pons-Winnecke and
Bielids). In dealing with the relations between comets and meteors two
other major factors have to be considered. Firstly there are a number of
major showers for which there seems to be no possibility of a cometary
relationship—these are considered in§ 3 below. Secondly there are a large
number of comets which, on the basis of Table 167, might be expected to
give rise to meteor showers. Lists of such comets approaching the earth’s
orbit within 0-25 a.u. were drawn up in 1875 by Herschelf and in 1920
by Davidson. J Porter has considered the matter again recently.§ There
are some sixty-eight cases of long period or parabolic comets which
should approach the earth sufficiently closely to produce a meteor
stream but there are no major showers which can be associated with
these. For comets moving in elliptical orbits of date later than 1700,
approaching the earth to within 0-1 a.u., Porter gives the data listed in
Table 168. Of the nineteen cases in this Table there are only six close
relationships of the classic type, together with a highly probable associa¬
tion (the Ursids) and a doubtful relationship (the 77 -Aquarids). Occasion¬
ally, claims are made for the association of a minor shower with a
cometary orbit, and at one time Denning published a list of twenty-eight
such accordances. These have never received independent confirmation
and, moreover, it seems very likely that many of Denning’s minor
streams represent fictitious groupings of sporadic meteors.
The failure to find meteor streams associated with the majority of the
elliptical comets in Table 168, and for sixty-eight parabolic comets with
equally close approaches, and the existence of several major showers
without parent comets (see § 3) has led authors such as Porter|| to urge
caution over the widespread view that meteors are the debris of comets.
The possible mode of formation of meteor streams from comets in the few
cases where the connexion is clearly established will be discussed in § 4.
t Herechol, A., Rep. on Meteors to Brit. Assoc., 1875.
X Davidson, M., Mon. Not. Roy. Astr. Soc. 80 (1920), 739.
§ Porter, J. G., Comets and Meteor Streams (Chapman & Hall, 1952); J. Brit. Astr.
Assoc. 62 (1952), 101.
|| Porter, J. G., ibid.; Rep. Phys. Soc. Proyr. Phys. 11 (1948), 402.
XXI, § 1
OF METEORS
415
Table 168
Comets with Elliptical Orbits approaching the Earth to within 0-100 a.u.
Comet
Period
[years)
Possible
meteor
radiant
Date
Closest
at longi¬
tude
Distance
oj closest
approach
( Comet-
Earth )
Remarks
1819 IV Blanpain .
6 1
H0
Jan. 9
ft+ 29’
a.u.
+ 0 077
• •
1743 I .
5-4
350 -10
Feb. 11
ft+ 62°
+ 0026
• •
1907 II Grigg-Mcllish .
164
308 -61
Mar. 30
a
-0002
• •
1861 I ...
417
271 +34
Apr. 21
a
-0 002
Lyrida (see
Grigg-Skiellorup .
60
109 -37
Apr. 26
a
-0 098
Table 167)
Halloy .
76-3
336 -1
May 6
v-n*
-0064
i)-Aquarids( T)
1930 VI Schwossmann-
Wachmann
5 4
218 +45
Juno 8
15
+ 0 006
(bco Tablo 167)
Pons-Winnccko
6 1
204 +66
Juno 30
IS
+ 0028
Pon»-Winnecko
1770 I Lexell
n
273 -21
July 6
15- 32*
+ 0015
(aco Table 167)
1862 III
45 +58
Aug. 11
15
+ 0010
Pcr80id9 (boo
Finlay ....
■9
278 -37
Sopt. 29
peri
+ 0 055
Table 167)
• •
Giacobini-Zinner .
66
262 +54
Oct. 10
15
+ 0 004
Giacobinids
1866 I Torapol
332
147 +24
Nov. 11
IS- 4*
-0 024
(bco Table 167)
Leonids (bop
1743 I .
5-4
22 +4
Nov. 14
a-39*
-0021
Tablo 167)
e •
1852 III Biela
MU
23 +42
Nov. 28
15- 2*
+ 0008
Biolida (boo
1770 I Loxell
M
256 -25
Dec. 5
a-62’
Tablo 167)
• •
1917 I Mcllish
145
103 +9
Dec. 15
a-5*
-0061
• B
1881 V Denning .
8-5
277 -35
Dec. 17
a+18*
+ 0037
• •
1926 IV Tuttlo .
13-5
219 +74
Dec. 22
15
+ 0100
Ursida (boo
Tablo 167)
2. The case of Encke’s Comet and the November Taurid and
day-time /3-Taurid meteor streams
Encke’s Comet, although of short period, does not appear in Table
168, since the distance of approach > 0-1 a.u. Whipple's work on the
orbits of the Taurid meteors, described in Chapter XV showed that the
orbits of these meteors were remarkably similar to that of the comet
with respect to a, e, and tt, but that the planes of the comet and the
meteor orbits differed by 10° to 15°. Later, as described in Chapter
XVIII it also became clear that the day-time ^-Taurid meteors of June-
July moved in similar orbits to the November Taurids. The discrepancy
in the inclinations apparently removed all possibility of a common origin
or connexion between these meteors and Encke's Comet, the first
criterion given in § 1 not being satisfied. However, the stream makes
close approaches to the terrestrial planets, and by studying the effects
416
COSMOLOGICAL RELATIONSHIPS
XXI, §2
of successive perturbations, particularly by Jupiter, Whipplef has been
able to show that a common origin of Encke’s Comet and the Taurid
stream is probable.
The ratio of the periods of Encke’s Comet (3*3 years) with the period
of Jupiter (11-86 years) is nearly 2 to 7; hence at aphelion a near approach
to Jupiter occurs every seven revolutions (about 1 a.u. minimum). In
his approximate theory of the secular perturbations, Whipple assumes
that the observed perturbations arise from this cause only, and that the
elements a and e are statistically constant with time.}: The systematic
changes with time in the angular elements co , ft, and i are given in Table
169.
Table 169
Observed Perturbations for Encke's Cornel
Difference in mean date
Aw
Aft
Ai
deg.
deg.
deg.
1812(2) to 1832(7)
+ 0-38
-019
-0-24
1832(7) to 1855(7)
+ 0-65
-0-43
-0-25
1855(7) to 1873(4)
+ 0-20
-0 10
+ 001
1873(4) to 1891(7)
+ 0-30
-016
- 0-22
1891(7)to 1914(7)
+ 0-71
-0-49
-035
1914(7)to 1931(3)
+ 0 26
-000
-000
Mean perturbation.
+ 0-42
-0 25
-018
Standard deviation
±021
±016
±014
With the notation of Chapter XX, § 1, the perturbing forces
S, T, W per unit mass due to Jupiter will be given by
(•)
T -< 2 >
* - HH) (3>
where m is the mass of Jupiter, k 2 the Gaussian constant, f, rj, and £
the coordinates of Jupiter with origin at the sun (oriented with respect
to the comet’s orbit in the sense 3, T, W), r and t 1 the radii vectores of
the comet and planet respectively, and p the distance between the
comet and Jupiter. Within the limits of accuracy desired the mean
t Whipple, F. L., Proc. Amer. Phil. Soc. 83 (1940), 711.
x In fact, the orbit shows an abnormal decrease in a which has been the cause of
much speculation. Whipple (Astrophye. J. Ill (1950), 375) has recently given a new
theory of this abnormality.
XXI, §2
OF METEORS
417
value of the tangential force T can be taken as zero, also the solar
attractions f/rj and J/rJ can be absorbed in a constant k 0 together with
k hn. A mean value of 1/p 3 can then be found such that the value of £
exactly at aphelion of the comet and opposition of Jupiter may be used.
The longitude of Jupiter then becomes (7r-f 180°) and
£ = ^ sin a/sin i' (4)
(to ', i', SI', etc., are the elements of the comet reduced to the plane of
Jupiter’s orbit).
With these approximations (1), (2), and (3) become
From standard theoryf the perturbations in n, SI', and i' are given by
na 3 / 2 Vp^= — ^cosi'S-f tt^sin vT-\- rsinu-^j-,
,, 2 , A SI' sint* f7 ,
"a^Vp-f = r—
( 6 )
(7)
na 3,a Vp^- = r cos u W, (8)
At
where v is the true anomaly of the comet, u its longitude from the ascend¬
ing node, n the mean motion, and At the effective time for which the
forces act. p is the semi-latus rectum = a(l—e 2 ).
On the assumption that the perturbations occur at aphelion, v = 180°
and u = a/ 180 °. Substitution in equations (6), (7), and (8) combined
with equations (5) give
t For example, Moulton, F. R., i4n Introduction to Celestial Mechanics (Macmillan,
1923), p. 404.
3695.88 E 6
418
COSMOLOGICAL RELATIONSHIPS
XXI, §2
The second term in (9) is numerically small and may be neglected.
T his equation and (11) may be used without further modification to
obtain average values of the perturbations per close approach ; but in ( 10 )
the sin 2 o/ term will be inaccurate when sin a/ is near zero. Whipple
averages sin 2 o/ over a range l in longitude on each side of aphelion and
replaces sin 2 o/ by J(l— k 3 cos2a/) where k 3 = sin2J/2J is determined
from the observed mean ratio of A&'/Ai' per close approach.
Finally for the fundamental equations Whipple obtains
un .
— = k.
&7T
dt
djy
dt
da/
dt
dr
dt
= -k 2 (l-k 3 cos2o/)
= k 4 —k 5 cos 2a/
~ = —k 6 sina/ cos a/ sini'
( 12 )
where k 4 = ki+k 2 and k 5 = k 2 k 3 .
In these equations the unit of time is the average interval between
close approaches, and all quantities which are not angular elements are
combined as constants (k t , etc.). Integration of equations (12) then gives
TT
cos2a/
SI' =
log tan-
n 0 +k x t
k 5 —k 4 sink 7 (t—1 0 )
k 4 -k 6 sin k 7 (t-t 0 )
7T —a/
k 8 -k 9 log(k 4 -k 5 cos 2a>')
(13)
where 7T 0 , w' 0 and i' 0 are the values at t = 0 (1855) and where
k 7 = 2 V(kS-kJ),
sin k 7 1 0 =
k 5 +k 4 cos 2 ojq
k 4 —k 5 cos 2u)q'
• 9
k 8 = log tan ^ -f k 9 log(k 4 —k 5 cos 2u) 0 ) y
it
k 9 = k 6 /4k 5 .
From the mean values of the observed perturbations (Table 169) and
the initial values of the elements of the comet referred to Jupiter’s plane
XXI, §2
OF METEORS
419
(Table 170), the values of the constants as given in Table 170 are obtained.
The unit of time is the average interval between close approaches (about
21 years) and the zero of time is 1855.
Table 170
Elements of Comet Encke and three Taurid Meteors referred to Jupiter's
Orbit (1920) and the Values of the Perturbation constants
Comet
Encke
Meteor
642
Meteor
710
Meteor
778
Perturbation
constants
to
188°0
134-8
337-9
k, 0-00290
SI '
331 0
15-0
■
227-5
k, 0-0463
IT
158-8
149-8
169-7
k, 0-942
i'
Dihodral angle between orbit
139
5-7
m
4-5
k 4 0-0492
pi an ee of meteor and comet *
0-0
10-6
12-3
15-6
k t 0-0436
k, 0-0924
a(a.u.)
2-217
1-910
2-349
2-191
k, 0-0456
e
0-847
0-845
0-844
0-891
k T t 0 30°-6
Aphelion distance (a.u.)
■
3-52
4 33
4-14
t 0 11-7
k, -2-047
k, 0-530
The period of revolution of a/(4w/k 7 ) is 276 intervals or about 5,800
years, and the period of variation of i' is half that of a/, or about 2,900
years, and lies within the range i' = 16°-0 to i' = 3°-6. The perturbed
elements calculated as above are shown in Fig. 187 as functions of the
number of close approaches with Jupiter.
In associating the Taurid meteors with the comet, Whipple presumes
that at some stage in the past a remote comet disintegrated into smaller
ones and that the Taurid meteors are the disintegration products of one
or more components of the original. In this case the relation between co'
and i' obtained above for the comet should also apply to the Taurid
meteors. The appropriate calculations carried out as above for meteors
Nos. 642, 710, and 778 give values for the inclination i' of 5°-l, 3°-9,t
and 4°-5f respectively, in very good agreement with the observed values
(Table 170) of 5-7°, 4-5°, and 4-5°. It appears, therefore, that the only
serious discrepancy in the orbits of the Taurid meteors and Encke’s
Comet—that of the inclination—can be explained satisfactorily in
terms of perturbations due to close approaches with Jupiter at aphelion.
t According to Brouwer ( Astr. J. 52 (1947), 190), the correct calculated values for
meteors 710 and 778 should be i' = 4°-5 and 8 e -7 respectively, the original values of
i' = 3°-9 and 4’-5 being in error due to a numerical slip. This correction worsens some¬
what the agreement in the calculated inclination of 778 with the observed value.
420 COSMOLOGICAL RELATIONSHIPS XXI, § 2
Subsequently Brouwerf carried out a more rigorous treatment of the per¬
turbation theory as applied to Encke’s Comet, and confirmed the results
obtained by Whipple in the approximate empirical theory outlined above.
The perturbations depend on the aphelion distance of the orbit and
Whipple points out that it should be possible to estimate the times
elapsed since the separation of the meteor streams from the comet by
-ISOS -665 I7S IOIS /ASS 269S SSSS 437S
DaUAD
Fio. 187. Perturbed orbital elements for Encke’s Comet os calculated by
Whipple.
comparing a/ and SI' for the various orbits. Taking a mean aphelion
distance for the four best determined Taurids in the earlier work,
Whipple estimates a minimum value of 5,000 years from considerations
of the value of a/. Unfortunately this leads to a discrepancy in n which
should have changed by +15°, but for which the observed difference is
negligible. A partial reconciliation can be achieved by adjusting the
value of to ' but this leads to ages of from 5,000 to 20,000 years for the
four meteors in question. From other considerations related to deviations
between the correlations of the elements, Whipple obtains an age of
14,000 years. More recently the topic has been reconsidered by Whipple
and Hamid, J who have recalculated the secular perturbations on the
basis of Brouwer’s more rigorous treatment of the perturbation theoryf
f Brouwer, D., Astr. J. 52 (1947), 190.
j Whipple, F. L., and Hamid, S. E. D., Harv. Abstract (see also Sky and Telescope
9 (1950), 248).
XXI, §2
OF METEORS
421
including the later Taurid data obtained by Wright and Whipple f making
a total of nine meteors. For five of the orbits the values of n tend to
converge to the value of Encke’s Comet 6,000 years ago; and for three
orbits 7 t diverges appreciably. They also find that the orbit planes of
four meteors coincided well with that of Encke’s Comet 4,700 years ago,
and that three other orbit planes coincide with each other but not with
that of the comet, about 1,500 years ago. They also find that the 4,700-
year orbit set tends to cross near the solar distance 3.0 a.u. before
aphelion, and those of the 1,500-year set near aphelion.
From these facts Whipple and Hamid conclude that the meteor streams
were formed by a violent ejection of material from the comet some 4,700
years ago and by a subsequent ejection 1,500 years ago from a body
moving in an orbit of similar shape and 7 r, but with greater aphelion dis¬
tance—probably a component of the comet which split away at an
unknown time in the past. It is also concluded that the velocity of
ejection was about 3 km./sec.; and that the ejection occurred at a
distance r> q. These conclusions are not consistent with Whipple’s
theory of the mode of formation of meteor streams by cometary ejection
(see § 4 ), and the authors propose that the ejections from Comet Encke
were the result of encounters with asteroidal bodies. The calculated
points of ejection lie near the asteroidal plane, and one of the points is
in the region of the greatest concentration of asteroids.
The main conclusions arising from this theory of Whipple and his
associates is, therefore, that the complex system of Taurid-Arietid
streams active in October-November probably had a common origin
with Encke’s Comet several thousand years ago. Further, in view of the
similarity of the orbit of the day-time 0-Taurid stream with the autumn
Taurids, and of the day-time {-Perseid stream with the autumn Southern
Arietids it must also be presumed that two of the most prominent summer
day-time streams have a similar origin.
The above theory has been given considerable attention in this
chapter since it represents almost the only contemporary effort to
investigate in detail the complex problems surrounding the possible
association of meteor streams and comets. Moreover it presents a
probable solution of the origin of a series of prominent major showers.
3. The major meteor showers without cometary associations
The list of showers given in Table 167 as possibly associated with
certain comets omits several of the important major showers. These all
t Wright, F. W., and Whipple, F. L., Tech. Rep. Harv. Coll. Obe., no. 6 (1950).
422 COSMOLOGICAL RELATIONSHIPS XXI, §3
have orbits of short period and association with cometary objects seems
extremely unlikely. A list of the main showers in question, for which
orbits have been determined, is given in Table 171.
Table 171
Major Meteor Showers without Cometary Association
Meteor shower
Date
Radiant
a £
Semi-major axis
a (a.u.)
(T) Quod rant ids .
Jan. 3
230°
+ 60°
20
5-Aquarids .
July 28
340°
-17°
1-6
Geminids
Dec. 13
111 °
+ 32°
15
Arietids (day-time)
June 8
44
+ 24
16
o-Cetids (day-time)
May 19
29-4
-2-7
1-3
All the summer day-time streams appear to move in short period orbits.
The J-Perseid and 0-Taurids have been associated with Encke’s Comet
above, but the Anetids and o-Cetids have no cometary association and
are included in Table 171. The only two other streams in the summer
sequence for which velocities have been determined are the 54-Perseids
and 0-Aurigids, both with similar short period orbits, but these streams
have not been included since the data rest on measurements in one year
only. Of the night-time streams the Geminids and S-Aquarids have no
obvious cometary connexion. The Quadrantids were also included in
Table 171 as possessing a doubtful association with Comet Kozik-
Peltier. This could only be so if the comet ejected the Quadrantid
material at a particular point of its orbit, and at present the classification
of this stream must remain doubtful. Some similar doubt must exist
on the question of the Orionids, and 77 -Aquarids; but the nature of their
orbits and their connexion with Halley’s Comet is reasonable enough to
justify their inclusion in the cometary class. Although the number of
showers listed in Table 171 is less than those listed as possessing cometary
association in Table 167, nevertheless they include some of the showers
which are most prominent at the present time. The existence of such
great amounts of debris moving in orbits of short period presents one of
the most interesting aspects of meteor astronomy, for which at present
there is no satisfactory solution.
Whipple’s photographic studiesf first showed beyond doubt that the
Geminid meteors were moving in orbits which were unique compared
with the orbits of known comets, planets, and asteroids. The comet of
shortest known period, Encke’s, has a period of 3-3 years, or twice that
f Whipple, F. L., Proc. Amer. Phil. Soc. 91 (1947), 189.
XXI, §3
OF METEORS
423
of the mean period of the Geminids. Even the period of the unusual
asteroids Eros and Apollo is longer than the average Geminid. The
eccentricity of the orbit is also greater than that of any asteroid. As
regards the possibility of the Geminids having a cometary association it
is clear that a comet in the present Geminid orbit would disintegrate
rapidly owing to the frequent perihelion passages at such a small distance
from the sun. The small aphelion distance also makes it difficult to
account for the short period as resulting from the perturbing effect of
Jupiter. If it is assumed that the parent of the Geminid stream was
originally a member of the Jupiter comet family then some unknown
forces must have reduced its aphelion distance from about 5 a.u. to 2-65
a.u. It is possible that although the orbit now only approaches the
earth’s orbit closely, in the past it may have been oriented to permit of
large perturbations by Venus or Mars. The action of Jupiter on such an
orbit over periods of thousands of years might produce large changes
in the inclination in the same manner as discussed for the Taurid meteors
and Encke’s Comet.
Maltzevf considered the possibility that the Geminids were separated
from a parabolic comet by the close approach of the comet to the sun,
with specific reference to the great comet of 1680. The orbits are near,
a little after perihelion, in close proximity to the sun. PlavecJ has also
referred to certain perturbations of the Geminid orbit. He calculated
the secular perturbations in Whipple’s elements for the Geminid orbit
due to Jupiter and the earth over a hundred years with the results given
in Table 172.
Table 172
Perturbations of the Oeminid Orbit by Jupiter and the Earth in 100 years
and changes in the least distance of the Orbit from the Earth
Elements
epoch
1937
Secular perturba¬
tions by
Year
ft
Radius
vector
Distance
from
earth
Jupiter
Earth
7f 226° 02'
ft 260° 43'
i 23° 28'
o 0-900
a 1-396
A.D.
1700
1900
2100
264° 33'
261° 18'
258° 03'
- -
Dec. 17. 7
Dec. 14. 6
Dec. 11. 4
(a.u.)
0-8503
0-9665
1-0912
0-1337
0-0178
-0-1066
The rapid retrogression of the node is of particular interest, since it
would cause the date of maximum of the shower to change by one day
t Maltzev, V. A.. Astr. J. U.S.S.R. 8 (1931), 67.
X Plavec, M., Nature, 165 (1950), 362.
424
COSMOLOGICAL RELATIONSHIPS XXI, § 3
in sixty years. Also the point of intersection of the orbit with the plane
of the ecliptic does not move parallel with the earth’s orbit but cuts it at
a steep angle. This gives rise to a rapid change in the least distance of the
shower from the earth as listed in Table 172. Taking the width of the
debns as about 0-1 a.u., these calculations indicate that the Geminids
can only be visible for about 400 years, and that they probably appeared
about 1700 and will disappear about 2100. Plavec claims to have
established the retrogression of the node, and draws attention to the fact
that although at present the Geminids are one of the strongest showers
there is little reference to their occurrence even 100 years ago.
It will be evident from the above discussion that the origin of the
Geminid meteor stream remains an enigma, as does that of the remaining
streams listed in Table 171. As yet there has been no serious speculation
on the origin of the day-time o-Cetids, 8-Aquarids, and day-time Arietids
The remarkable similarity in the shape of the orbits of the two latter
streams has been referred to in Chapter XVIII, but their different
inclinations may present an obstacle to the idea of a common origin.
The topics discussed so far in this chapter have been investigated at
great length from a phenomenological aspect by Hoffmeister. f This
work is a major attempt towards a separation and classification of the
chief statistical components of meteor phenomena, which Hoffmeister
considers under the headings of ecliptical, cometary, and interstellar.
Although it is no longer possible to attach any significance to the idea
of an interstellar component, Hoffmeister’s classification under the other
headings agrees well with the contents of this chapter. He includes
many other streams which are not generally regarded as of a major
character in support of the classification. As regards the ecliptical
component, under which heading could be included the short-period
streams discussed in this section, Hoffmeister concludes that the system
is not related to comets but that it forms part of the system of minor
planets. The similarity of the orbits to some of the minor planets is
indeed striking, and the idea of a planetary origin for these short-period
meteor streams is both plausible and attractive. The question of these
short period orbits will be referred to again in § 5.
4. The mode of formation of meteor streams from comets
Although the cosmological associations for some of the major meteor
streams is obscure it would be hard to deny in view of the evidence
t Hoffmeister, C., Meteorstrdme, Weimar, 1948—a short summary is given by Hoff-
meistor in the Observatory, 70 (1950), 70.
OF METEORS
425
XXI, §4
presented in § 1 that at least some of the important meteor streams
appear to have a close association with comets. Evidently there are two
broad possibilities, either the meteoric debris is the primeval material from
which the comet is forming, or conversely, the debris is the result of some
disintegration process in the comet. In Chapter XIX it was estimated
that the total mass of meteoric material in the orbits of the major meteor
streams was about 10 12 kg. This is somewhat less than the cometary
masses—a recent estimatef of the mass of Halley’s Comet is about
10 16 kg.—and this fact would appear to favour the ejection or disintegra¬
tion hypothesis. The methods by which comets could give rise to meteor
streams appear to have been first discussed seriously by Schiaparelli
who formed the view that meteor streams arise from comets because of
the dispersive forces which occur when the comet makes close approaches
to tho sun or a planet. Later, Bredikhinc developed the ejection theory,
as mentioned in Chapter XX. A summary of these earlier ideas has been
given by Olivier.J The most recent and detailed theory of the formation
of meteor streams from comets is due to Whipple§ whose views will be
summarized here.
(a) Whipple's Comet Model
Whipple proposes a new comet model whose nucleus is visualized as
consisting of a conglomerate of ices such as H 2 0, NH 3 , CH 4 , C0 2 or CO,
C 2 N 2 , and other materials volatile at low temperature (< 50° K.), but
on approaching the sun, vaporization of the ices occurs through extern¬
ally applied solar radiation. This leaves an outer matrix of non volatile
insulating meteoric material. Meteoric material below some limiting
size will blow away because of the low gravitational attraction of the
nucleus, and will begin the formation of a meteor stream. Some of the
larger or denser particles may also be removed by shocks, but the largest
particles will remain on the surface to produce an insulating layer. After
a short time the loss of gas will be materially reduced by the insulation
provided by this matrix. Whipple shows that the heat transfer through
such thin meteoric layers in a vacuum is limited chiefly by the radiative
rate, and that it is inversely proportional to the effective number of
layers. It is shown that an appreciable time lag in heat transfer can occur
for a rotating cometary nucleus. The low central temperature is main¬
tained by vaporization of the ices. This cometary model is capable of
explaining the peculiarities in the orbital behaviour of certain comets.
t Vorontsov-Velyaminov, B., Astrophys. J. 104 (1946), 226.
j Olivier, C. P., Meteors , ch. 17.
§ Whipple, F. L., Astrophys. J. Ill (1950), 375; 113 (1951), 464.
420
COSMOLOGICAL RELATIONSHIPS
XXI, §4
For example, if the nucleus is rotating in the forward sense with respect
to its revolution, the time lag in heat transfer will result in the vaporized
ices being emitted with a component towards the antapex of motion.
The momentum transfer will propel the nucleus forwards, reduce the
mean motion and increase the orbital eccentricity, as observed for
comets such as C. Wolf and C. d’Arrest. Retrograde motion will produce
an acceleration in mean motion and a decrease in eccentricity as observed
for Comet Encke. Whipple shows that the present orbital changes could
be produced by a mass loss of from 0 002 to 0 005 units per orbital
revolution, provided the force is proportional to the solar energy flux,
and cuts off at a distance of about 2 a.u.
As regards the ejection of the meteoric material, Whipple considers
the material which has already been carried some distance from the
nucleus, in order to avoid the complicated forces which are likely to
arise near the surface. He assumes that the escape is sufficiently rapid
so that it is only necessary to consider the gases escaping from the sunlit
hemisphere. If the ices utilize a fraction 1/n of the solar radiation for
sublimation; if the nucleus is spherical of radius R c and density p c ; and
if the mean heat of sublimation of the ices is n calories per gramme,
then the mass of ices Am sublimated per second at a distance r(a.u.) from
the sun is given by
nllr*’ < 14 )
Am
where S is the solar constant (= 0 032 cal. cm.- 2 sec.- 1 at 1 a.u.).
At a distance R (> R c ) from the nucleus it is assumed that the gas
escapes over the hemisphere 2 ttR 2 with an outward velocity given by
where k is Boltzmann’s constant, T g the temperature and A the molecular
weight of the gas. The momentum transferred per second per square
centimetre at a distance R is then
(uER 2 )
(2nr 2 nR 2 )’ < 16 )
It is believed that meteoric particles are irregular and rough and hence
will have a large accommodation coefficient for gaseous encounters. For
simplicity Whipple assumes the coefficient to be unity, and that the
particles are spherical of radius r and density If the cometary gas is
stopped by these particles and re-emitted immediately with thermal
OF METEORS
427
XXI, §4
velocities, the drag coefficient is approximately that for free molecular
flow.
Thus the outward force on a slowly moving particle is given by
137rur 2 HR* fY'j)
18nr 2 riR 2 *
The total force will be reduced by gravity so that the net outward
acceleration becomes
d 2 R (C,—C,R c )R 2
(18)
dt 2 R 2
where
39uE
1 72nr 2 rp,n
(19)
and
C 2 = 4^p c |-
(20)
The relative velocity V* of the particle at infinity with respect to the
cometary nucleus is then given by
V 2 , = 2C 1 R c —2C 2 R?. (21)
Whipple shows that a reasonable value for the gas temperature T g in
(15) is T g = 300/Vr °K. giving
u — / 8 x 300° K- U_1_ (22)
\ "A / (r,. n .)<
Taking />„ = 1 gm. cm.-*, p, = 4gm. cm.- 3 , A = 20 x 1-661 X 10- 2 *gm.,
and expressing r in cm., R c in km., and r in a.u. equation (21) reduces to
V B = 0 052 R c ^ R* 328 cm. sec.-» (23)
As an example of orders of magnitude of V w Whipple considers the
case of a new comet for which the sublimation efficiency n is unity, of
radius 1 km. at distance 1 a.u. from the sun. Meteoric particles of radius
1 cm. and density 4 gm. cm. -3 would be ejected with a velocity of about
3 metres per second.
Equation (23) indicates that the ejection of meteoric debris should be
more violent and frequent near perihelion. Also, for the same (1/n),
large comets should eject particles with greater velocities than small
comets. Whipple uses this prediction to assess the theory in terms of the
frequency of bright meteors as represented in the Harvard photographic
collection and gives the data of Table 173.
428
COSMOLOGICAL RELATIONSHIPS
XXI, §4
Table 173
Relation of Comet Brightness and Meteor Characteristics
Meteor shower
Associated
comet
Comet
brightness
q (a.u.)
Shower
length
(days)
Nature of
photographed
meteors
Pereeids
Leonids
Lyrids .
Bielids .
Geminids
17 -Aquarids .
Orionids
Giacobinids .
Taurida
S-Aquarida
Quadrantids .
1862 HI
1866 I
1861 I
Biela
?
Halley (T)
Halley (?)
1933 HI
Encke
?
?
Bright
Lost
Bright
Lost
Bright
Bright
Faint
Medium
• •
• •
0-97
0-98
0-92
0-86
014
0-69
0-69
100
039
004
0-99
30
6
4
6
4
6
10
1
40
10
2
Strong
Medium
Weak
Weak
Strong
Weak
Medium
Weak (?)
Strong
Strong
Weak
In general the predictions of the theory are confirmed—the most
widely dispersed showers like the Perseids and Taurida, and possibly the
ij-Aquarids and Orionids, arising from massive comets; while the faint
comets—Giacobini-Zinner, Biela, and 18661 produce concentrated
showers. The evidence is not conclusive since large comets have pro-
duced concentrated showers, on the other hand all the faint comets in
Table 173 have produced concentrated showers.
The maximum radius r m „ of ejected meteoric material can be obtained
from equations (18-23) as
fm “ = JsSg; cm ' ( 24 >
where R c is in km. and r in a.u.
The maximum radius is sensitive to the perihelion distance, and for
close approaches corresponds to extremely bright fireballs. In Table 173
there are three perihelion distances less than 0-6 a.u. and in each case
the showers are strong photographically. From a perusal of the von
Niessl-Hoffmeister fireball catalogue (Chapter VKI) Whipple also
concludes that the showers with smaU perihelion distances definitely
tend to show unusually bright meteors.
It is clear that Whipple’s new theory offers a most promising approach
to the problem of the physical relationships of meteors and comets. More
precise testing of the theory should rapidly become possible as the new
photographic and radio-echo data on meteors accumulates.
(6) The Ejection and Evolution of the Perseid Stream from Comet 1862 III
The prominence, age, and clear association of the Perseid meteor
stream with Comet 1862 III has always attracted much interest in regard
OF METEORS
429
XXI, §4
to the mode of formation of such an extensive region of debris from the
comet. The first serious speculations appear to have been made in
the nineteenth century by Bredikhine, who, as mentioned previously,
favoured the theory of ejection of the meteoric matter from the comet ary
nucleus. Schulhof considered that such ejections could not possibly
form such an extensive stream as the Perseids without planetary per¬
turbations. The most recent treatment along these lines is by Hamid,t
whose work on this subject has been mentioned in Chapter XX. On
the basis of Whipple’s comet model, Hamid calculates the velocity of
ejection of the Perseid meteors from the comet to be 16-5 metres per
second. A few dozen revolutions would suffice for the ejected material
to be scattered around the orbit but without perturbations the shower
would be very short « 1 day). On the basis of Whipple’s model the
ejection will occur at an appreciable rate only when its distance from the
sun is 2 a.u. or less. It is therefore necessary to calculate how long it has
been since the comet’s perihelion distance was within 2 a.u. of the sun.
Hamid shows that the comet must have been captured by Jupiter and
that the ejection of the meteors occurred after capture. By a detailed
treatment of the effects of the perturbations due to Jupiter and Saturn
he concludes that the present configuration of the stream could arise
from an ejection which took place about 40,000 years ago.
5. The origin of sporadic meteors
A good deal of attention has been given earlier in this book to the
problem of the velocity of sporadic meteors, and the conclusion now
seems inescapable that they must be contained in the solar system
as distinct from the interstellar view which has prevailed for so long.
Perhaps of equal significance is the increasing amount of evidence from
the radio-echo and photographic data that their orbits, far from being
hyperbolic, are in fact of short period, and bear more resemblance to
the orbits of the ‘planetary’ shower meteors discussed in § 3 than to the
longer period orbits of the cometary shower meteors. WhippieJ drew
attention to this peculiarity in the first publication of the accurate
photographic results, which included the orbits of four sporadic meteors.
Three of these had orbits only slightly inclined to the ecliptic and of
short period. The fourth had retrograde motion in an orbit of long period.
Whipple pointed out that the first type of orbit was similar to the orbits
of the asteroids with perihelion distances less than unity, and emphasized
t Hamid, S. E., Doctoral dissertation (Harvard, 1950).
X Whipple, F. L., Proc. Amer. Phil. Soc. 79 (1938), 499.
430
COSMOLOGICAL RELATIONSHIPS XXI, §6
this peculiarity by compiling the data given in Table 174. This table
gives the orbital elements for the three sporadic meteors in question, the
three asteroids with perihelion distances less than unity and the'five
comets of periods less than seven years and perihelion distances less than
umty. The orbital similarities between the asteroids and the meteors
are most marked. Subsequently, similar types of orbits were found for
several major showers as discussed in § 3, and recently, as mentioned
above, there are now very strong grounds for believing that the orbits of
many of the sporadic meteors are of this asteroidal type.
Table 174
Comparison of the Orbits of Short-period Sporadic Meteors, Asteroids,
and Cermets
Sporadic meteors
q
a
e
i
Whipple No. 642f
0 296
1 91
0*84
deg.
60
Whipple No. 660.
0968
2-22
0*56
4*3
Whipple No. 670.
0618
321
0-81
1-9
Mean
0627
245
0-74
4*1
Asteroids (q < 1)
Apollo t
0647
1*48
066
6 4
Anteros§ .
0 441
1 86
0*76
1*4
1937 UB|| .
0*618
1*64
063
6 2
Mean
0569
1*66
065
4*7
Comets ft (P < 7 years: q < 1)
Encke . . . ;
0 332
2*21
085
12*6
Grigg-Skjellerup.
0*908
2*93
0*69
17*4
Brorsen I .
0*590
3-11
0*81
29*4
Giacobini-Zinner
1 000
3 52
0*72
30*7
Biola ....
0*856
3*52
0*76
12*6
Mean
0737
3*06
0*77
20*5
The questions raised by these remarks and the contents of § 3 may be
of deep significance in studies of the origin of the solar system. It may
be anticipated that during the next decade a large amount of accurate
information will be obtained by photographic and radio-echo studies,
on the orbits of individual sporadic meteors. In this case the basic
l 642 waa subf *quently classified as a Southern Arietid (see Chap. XV)
♦ ** h, PP l0 . F- L-. and Cunningham. L. E., Ann. Harv. Coll. Obs. 105 (1937) 637.
§ Hergot and Miss Davis, Harv. Announcement Card (1936), no. 366.
|| Cunningham, L. E.. ibid. (Jan. 1938), no. 440.
tt Yamamoto, A. S., Pub. Kwasan Obs. 1 (1936), no. 4.
OF METEORS
431
XXI, §6
material will be available for a detailed theoretical study of the origin
of these short-period meteors. The major problem to be settled is whether
these meteors are the debris of the primeval matter from which the solar
system was formed, or whether they are the result of some subsequent
planetary or cometary break-up. In this connexion it is interesting to
notice that the Poynting-Robertson effect sets a rather short time-scale
at which any such break-up could have occurred. The mean semi-major
axis for the asteroids is about 3 a.u. and if the sporadic meteors were
formed by a planetary disintegration at about this distance from the
sun their orbits would mostly be within that of Jupiter with an apse near
the planet *8 orbit. Wyatt and Whipple f have calculated the times of
fall into the sun of particles with radius r moving in orbits of this type
assuming their density to be 4 gm./c.c., according to the method given
in Chapter XIX. Their results for various possible types of short-period
orbits are given in Table 175.
Table 175
Times of Fall into the Sun for Meteors with an Asteroidal Type of Origin
Perihelion
distance
q ( a.u .)
Aphelion
distance
q' (a.u.)
Semi-major
axis
a (a.u.)
Eccentricity
e
Constant C
equation 19
Chap. XX
Time of fall
t (years)
6
6
6
000
..
70 X 10 T X r
3
3
3
000
• •
25 x 10 T X r
3
6
4
0-25
114
llxlO’xr
1
3
2
0-50
2-60
1-9 x 10’ x r
1
6
3
0-67
2-31
2-9 x 10 7 x r
It can be seen from this table that for a time-scale of 3 X 10 9 years all
bodies with radius of less than 4 cm. must have been swept into the sun.
For a planetary break-up occurring 6x 10 7 years ago, as suggested by
BauerJ particles originating in the asteroidal belt of radius less than
0-08 a.u. must have been swept into the sun. Similar calculations have
been made by Opik§ who also introduces another important factor—
that of the filtration of the particles through collisions with the planets.
According to Opik’s calculations Jupiter presents a major obstacle, and
within the cosmic time-scale will have cut off practically all particles
over 2 mm. in diameter, although letting through fairly well those of
0-2 mm. diameter. If this view is correct then no meteor within the visual
f Wyatt, S. P., and Whipple, F. L., Astrophys. J. Ill (1950), 134.
X Bauer, C. A., Phys. Rev. 74 (1948) 501.
§ Opik, E. J., Proc. Roy. Irish Acad. 54 (1951), 165.
432
COSMOLOGICAL RELATIONSHIPS XXI §6
and normal telescopic range of observation can belong to the primordial
dust, but must have a more recent origin.
Such considerations imply a lack of faint meteors and militate against
the idea of an origin in the asteroidal belt within a reasonable time-scale.
If the primeval, or planetary, type of origin has to be abandoned for these!
or other reasons, then the possibility of dispersion from the orbits of the
cometary shower meteors presents an alternative. Although at first
sight a highly plausible source for sporadic meteors, we have already
seen earlier in this chapter the difficulty of explaining the evolution of
large amounts of meteoric debris moving in short period orbits, from a
cometary type of parentage.
6. Meteors and the zodiacal light
Although various theories have been advanced to account for the
zodiacal light there can be little doubt that it is due basically to an
extensive cloud of particles lying in the plane of the ecliptic and illumina¬
ted by the sun.f The evidence that this cloud of particles lies in the solar
system is also conclusive. Recent treatments of the problem by Allent
and van de Hulst§ in which the importance of diffraction of sunlight by
the zodiacal particles is emphasized, as well as scattering, has led to
speculations of considerable interest. Both authors show that one part
of the light of the solar corona (the Fraunhofer component) can be
explained as due to diffractional scattering by small zodiacal particles.
Allen’s solution requires a particle density of 2 x 10"“ gm. c.c. at 1 a.u!
from the sun on the assumption that the particles are of radius 10- 3 cm.
Van de Hulst assumes a distribution of particle sizes similar to that found
in the meteoric matter and his solution requires a particle density of
5x 10- 21 gm. c.c.; throughout the interplanetary medium with a thick¬
ness perpendicular to the plane of the ecliptic of about 0-1 a.u. Evidently
van de Hulst’s solution, involving a plausible distribution of particle
sizes appears preferable. Here we are particularly concerned with the
relation of this interplanetary matter, responsible for the zodiacal light
and the Fraunhofer component of the corona, to the meteorio matter in
the solar system.
Van de Hulst’s solution requires a density some 10 4 times greater than
that of meteoric matter in the solar system inferred in Chapters VII and
XIX. The preferred radii for the van de Hulst particles is between 1 mm.
t A convenient summary of the various views on the zodiacal light is given by Mitra,
S. K., m The Upper Atmosphere, ch. 10, Royal Asiatic Society, Bengal, 1948.
t Allen, C. W., Mon. Not. Roy. Astr. Soc. 106 (1940), 137.
§ van de Hulst, H. C., Astrophya. J. 105 (1947), 471.
XXI, § 6
OF METEORS
433
and 0*1 mm. and hence on the basis of his analysis faint meteors should
be 10,000 times more plentiful than actually observed. Van de Hulst
considers that his figure for the number of particles required to explain
the zodiacal light and the Fraunhofer component is unlikely to be in
error by a factor of 2, and even if one allows a factor of uncertainty of
10 or more in the meteor densities there is still a very large discrepancy
to be explained. He considers a possible explanation to be that only
a very small fraction of the interplanetary particles have velocities
high enough to cause visible meteors, and suggests that the majority of
the particles might move in nearly circular orbits similar to the planets
and asteroids.
In an interesting comment on this idea Opikf points out that van de
Hulst’s explanation of the discrepancy cannot be correct for the follow¬
ing reasons. Considering a two-body problem where the particles are
subject only to the attraction of a planet of mass m and radius r ; the
number of particles intercepted by a planet in unit time is
7T(J 2 pU,
where a is the effective target radius for capture, u the relative velocity,
and p the space density, a is the distance of the asymptote of the hyper¬
bolic orbit from the centre of the planet when the periastron distance is
r p . Then the velocity in periastron is
U = V(u 2 -f-£ 2 ),
where S, the velocity of escape from the surface of m, is given by
Conservation of angular momentum gives
au = l/r p
hence a 2 = r 2 -f-
and the intensity *F of a meteor shower produced by the cloud and inter¬
cepted by m becomes
'F is a minimum for u = S and approaches infinity as u -> co and as
u 0. Thus the condensing action of the planets gravitational field
would, in fact, give rise to a meteor shower of infinite intensity from the
f Opik, E. J. (1951), loc. cit.
Ff
3596.68
434 COSMOLOGICAL RELATIONSHIPS XXI, §6
‘quiescent cloud’ proposed by van de Hulst. In the case of the earth
the problem is complicated by the presence of the sun, but Opik shows
that the broad considerations are not changed. Opik’s own explanation
is that meteors of radius 6 > r > 10" 2 cm. must be practically absent
near the four inner planets, owing to the sweeping action of Jupiter
combined with the Poynting-Robertson drift. On the other hand, for
particles of radius ^ 10 -3 cm. Opik calculates that the drift is too fast
for the sweeping action of Jupiter to be significant. The time-scale in
these calculations is 3x 10® years. If this view is correct, particle sizes
of 10~ 3 cm. and less might well predominate in the zodiacal light particles,
whereas those in the range 0-03 to 6 cm. would be scarce. Much larger
particles, at present in the vicinity of the earth, probably originated
in the asteroidal ring, and hence might be expected to be relatively
plentiful. Opik’s suggestions therefore give an explanation of the dis¬
crepancy between the space density of interplanetary matter calculated
from the observed meteor frequency and that actually believed to exist
according to van de Hulst’s zodiacal light theory. A crucial test of van
de Hulst’s theory and of Opik’s views would be the observation of very
faint meteors of magnitude 16 to 20. These would correspond to the
particles of radius < 10- 3 cm. which escape the sweeping action of
Jupiter and would therefore be expected to be some 10,000 times more
numerous than predicted from the extrapolation of the number distribu¬
tion of visual meteors.
APPENDIX I
NOTE ON SYMBOLS
The notation for the most frequently recurring quantities have been standardized
as listed below.
VELOCITY
V always refers to heliocentric velocity of meteors.
V apparont volocity of meteor outside earth’s atmosphere.
V E orbital velocity of earth.
Vr rotational velocity of earth.
V heliocentric velocity of interstellar particle.
V mean heliocentric velocity corresponding to centre of radiation
(Chap. IX).
v geocentric velocity of meteor.
v p geocentric parabolic velocity of meteor,
v, geocentric velocity corrected for zenithal attraction.
v 0 velocity at mid-point of trail,
v' mean group velocity (Chap. XII).
v percentage speed (Chap. X).
v discreto values of spaco velocity (Chap. IX).
v velocity of interstellar particle.
iv (with suffix) angular velocity (Chap. IX)
w theoretical angular velocity (Chap. IX).
U orbital velocity of particle (Chap. XX).
U velocity of particle in periastron (Chap. XXI).
u velocity of comotary ejection (Chap. XX).
P - V B /V.
A = v/V E .
A 0 = V/V E (= 1 hi).
ORBITAL ELEMENTS
SI ascending node.
7S descending node,
i inclination,
a sorai-major axis,
b semi-minor axis,
e eccentricity.
q = a(l —e) perihelion distance,
q' = a(l-fe) aphelion distance,
p = a(l —o l ) semi-lalus rectum
oj angle of perihelion.
7 r = (il+o>) longitude of perihelion.
T time of perihelion passage.
v true anomaly.
M mean anomaly.
n mean daily motion in degrees.
t date.
436
APPENDIX I
<p angle of eccentricity (e = sintp).
E eccentric anomaly.
H hour angle.
P period of orbit.
MISCELLANEOUS ASTRONOMICAL NOTATION
8
p
A
A.
€
a
V
X
r
4 >
+
w
(occasionally R.A.) right ascension
(occasionally decl.) declination
fin the case of a meteor radiant
| the coordinates are printed in
the text as a 90°, 8+16°;
indicating right ascension 90°,
l declination +16°.
latitude of radiant (used as altitude of radiant in Chap. XII).
longitude of radiant,
longitude of apex.
elongation of radiant (A« elongation correction),
obliquity of ecliptic,
elevation of point on ecliptic,
distance from radiant.
zenith angle,
vernal equinox,
elevation of apex.
latitude.
period of axial rotation.
z measured zenith distance,
z corrected zenith distance.
2 solar constant.
6 earth-sun distance,
m magnitude.
m meteor mass,
r meteor radius,
m used for mass (unspecified).
r e radius of earth.
r t radius of earth’s atmosphere.
L length of meteor path.
M mass of sun.
O longitude of sun.
RADIO NOTATION
a r phase.
0 \
^ J polar diagram angles.
A wave-length.
<7 mean power density.
r pulse width (r 0 time in c.w from fj to f,).
co received power.
w 0 basic receiver noise level,
to wave frequency.
ip phase difference,
f! f a transmitter frequency.
APPENDIX I
437
f 0 pulse recurrence frequency.
G aerial power gain.
E„E(x) field strength.
I r intensity reflected wave.
N noise factor.
P transmitter power.
P e external noise.
W 0 power density.
W mean transmitter power.
Z echo amplitude (signal noise ratio).
MISCELLANEOUS NOTATION
c velocity of light,
e electron charge,
g acceleration due to gravity,
h height.
k Boltzmann’s constant, also k* = y (gravitational constant).
1 latent heat of evaporation,
m electron mass,
n rate of evaporation.
p atmospheric pressure,
t time.
t time relative to point.
t interval in days.
A atomic (molecular) weight.
D diffusion coefficient.
O Avogadro’s number.
H scale height.
/ luminosity.
1/L heat absorption coefficient.
a 0 no. of electrons per cm. path in meteor trail.
N no. of electrons.
T temperature.
S T W attractive forces.
y gravitational constant.
Ho = yM.
jx = y(Af+m) acceleration at unit distance,
p* acceleration at unit distance from earth.
II heat of sublimation.
p density.
APPENDIX II
SUMMARY OF RECENT WORK
The main part of the text was written towards the end of 1961 and early 1962.
In this Appendix a summary is given of subsequent results which became
available up to the end of 1963.
CHAPTER IV
1. A new radio-echo technique for the measurement of the orbits of single meteors
The radio-echo techniques for the measurement of meteor radiants described
in Chapter IV are applicable only to shower meteors or to rare single meteors of
exceptional brightness. At Jodrell Bank, Davies and Gillf have recently extended
the velocity measuring technique of Davies and EllyettJ to the delineation of
both radiants and velocities of individual meteors. In addition to the transmitter
and receiver used for the velocity measurements, two further receivers are
employed, spaced about 4 km. east and south of the home station. The echoes
received at these stations are transmitted by radio link to the home station where
they are photographed alongside the direct echo on a single film. Thus in addition
to the diffraction pattern yielding the meteor velocity, the time displacements
between the occurrence of the pattern at the three receivers can be measured,
and these time displacements lead to a knowledge of the meteor radiant. Since
the separation of the receivers is of the order of a length of a Fresnel zone, meteors
yielding velocity measurements on one receiver do so on all three. The accuracy
m velocity measurement is about 2 per cent, and in radiant position about 2°.
A preliminary experiment on the Geminid meteors in 1953 December yielded
orbits in good agreement with those obtained by Whipple.§ The method is now
being used to study the orbits of sporadic meteors. Between one and two hundred
orbits can be obtained in the course of 24 hours.
2. The radio echo from the head of a meteor trail
On pp. 73, 74 it was mentioned that no satisfactory explanation existed for
the occasional echoes observed from the head of the meteor trails, used for velocity
measurements by the range-time method. An explanation in terms of the
diffraction theory given in Chapter IV has now been offered by Browne and
Kaiser.|| No assumptions are invoked beyond those commonly accepted as
necessary to explain the specularly reflected echo. The theory predicts intensities
of the head echo in agreement with observation. It also predicts that the
intensity of the head echo relative to that of the specularly reflected echo should
be proportional to the radio wave-length and inversely proportional to the
difference in range between the two echoes.
CHAPTER VI
Visual work on the distribution of sporadic meteor orbits
On pp. 108 et seq. reference was made to the visual work of Prentice and the
B.A.A. observers on the distribution of sporadic meteors. The analysis has now
t Davies, J. G., and Gill, J. C. Not yet published.
t See Chap. IV, p. 78. § See chap. xv
|| Browne, I. C., and Kaiser, T. R., J. Atmos. Terr. Phys. 4, (1953), 1.
APPENDIX II
439
been completed but not yet published. The final analysis for 1,000 meteors
confirms the longitude and latitude distribution of apparent radiants shown in
Figs. 61 (a) and (6), and of the true radiants shown in Fig. 69.
CHAPTER XI
The double camera investigation of the velocity distribution of sporadic meteors
In a footnote on p. 211 reference was made to the fact that the Super Schmidt
cameras were working satisfactorily in September 1952. Unfortunately no results
of the investigation are yet available for publication, but according to private
information from Dr. F. L. Whipple and Dr. L. G. Jacchia the results are con¬
sistent with the distribution derived from the radio echo work (Chapter XII).
CHAPTER XIII
1. The Quadrantid shower
The text refers to the visual data collected by Prentice for the years 1921 to
1940. In a recent paper Prenticef has now published his observations for the
years 1941 to 1953. A new determination of the epoch of maximum gives
O = 282° 53' in close agreement with the previous value. The paper also
contains a discussion of a possible 13-year period in the activity.
In 1952 Alcock and Prentice $ succeeded in determining 13 Quadrantid radiants
from duplicate observations. The results show a spread in a from 231° to 243°
and in 8 from +40° to +60°.
A recent discussion of the orbit of the Quadrantid stream has been given by
Bou8ka.§ His calculations are based on the observational data given in the text,
and furthor consideration is given to the possible relationship of the stream either
with Comot Tuttle I or with Comet Kozik-Peltier.
Recently Millman and McKinley|| have published the results of a radio-echo
investigation of the 1951 Quadrantid shower, using the technique described in
Chapter IV. They obtain a mean geocentric velocity of 40-9±0-5 km./sec. Using
data on the radiant position obtained from other sources they calculate the mean
orbit with eccentricity 0-74, inclination 70°, and period 7-2 years, in goneral
agreement with the photographic and Jodroll Bank orbit described in Chapter
XIII.
2. The Lyrid shower
In view of the discrepancies in the position of the Lyrid radiant discussed on
pp. 261-2, some recent measurements in Czechoslovakia published by Ceplechatt
are of interest. Correction for zenith attraction has been made and the list should
bo compared with Table 85, p. 261.
The spread in the radiant position is evident and the measurements support
the conclusion of Prentice that the discrepancies cannot be due solely to errors of
observation.
| Prentice, J. P. M., J. Brit. Astr. Ass. 63 (1953), 175.
x Alcock, G. E. D., and Prentice, J. P. M., ibid. 186.
§ BouSka, J., Bull. Cent. Astr. Inst. Czech. 4 (1953), 165.
|| Millman, P. M., and McKinley, D. W. R., J. Boy. Astr. Ass. Can. 47 (1953), 237.
tt Ceplecha, Z., Bull. Cent. Astr. Inst. Czech. 3 (1952), 95.
440
APPENDIX II
Date
Radiant
No. of
meteors
a deg.
6 deg.
1947 April 20-66
273-3±0-7
+ 33-0±0-7
6
1947 April 21-75
273-2±l-l
36-6±0-7
9
1947 April 21-79
272-4±0-6
34-1 ±1-3
8
1947 April 21-79
279-5±0-4
37-3±0-6
6
1947 April 21-79
272-5±0-9
38-3±0-7
5
1947 April 22-23
270-8±0-0
35-0±0-0
3
1949 April 22-29
277-8±0-9
32-6±0-6
14
1949 April 22-29
273-3 ±0-8
34-7±0-5
14
1. The S-Aquarid shower
Rigolletf has published the results of telescopic observations of eight 8-Ao.mrM.
made m July 1951. The magnitudes range from +6 to +9. amUho commits
'irdbiaatT t m g r agreement with thMe * 91 <p- ^
mdbladt h«« discussed some implications of the short period orbit of the
of theTh* ’ P r rt :r y the le,n P erature e0ects to the closeness of approach
of the debns to the sun. He also refers to the possible occurrence of gaps iL the
velocay distribution which he suggests miglft be associated with^onJlce
oSS^JtSJ!: 0t M ^ant in
1948 July 30-34 a 337-7°±0-8°, 8-9-4°+1-0° (6 meteors!
1948 July 30-52 « 348-3° ± 0-8°, 8-lO-^i^ (6 meteom')-
These results, obtamed on the same night, are not in very good agreement with
the coordinates quoted in Table 91 (p. 272). greemont with
2. The Peraeid shower
Since the completion of Chapter XIV a number of important papers on the
Perseid stream have been published. In particular. Miss Wright and Whipplell
h Z:rZ ac0mpr ; he ™ ve amount of the Harvard photographic work on thi!
Chapter %7 der ^ ly eXt T d3 J he pr ® Ura “ , ary account of this work given in
Chapter XIV. The analysis is based on 115 photographs in the Harvard series
over the years 1893 to 1952 in the interval July 28 to August 24. Twenty-three
meteors were photographed simultaneously at two stations and ninety-two at
one station only. J
The mean radiant is found to be at a 46° 66', 8 +67° 45' (corrected) on August
1A at © 1M0 _ 139 0°. The daily motion is Aa 43'±2', AS 7'±2', in close
agreement with the values given previously in Chapter XIV. Table in in this
publication may be compared directly with Table 95 (p. 280) for the daily radiant
position. J
In the twenty-three doubly photographed meteors, eleven are used for orbital
t Rigollet, M. R., J. dea Obaervoteura, 35 (1952), 170.
X Lindblad, B. A., Observatory, 73 (1953), 157.
§ Ceplecha, Z., Bull. Cent. Aetr. Inst. Czech. 3 (1952), 95.
II Wnght, F W and Whipple, F. L., Tech. Rep. Harv. CoU. Obs. (1953), No. 11
(Harvard Repnnt Sories 11—47). V h
APPENDIX II
441
calculation. These include numbers 978, 1089, 1173, 1275, 1276, 1469, already
listed on p. 284, together with five other later reductions (2049, 2034, 2801, 2033,
2046). Numbers 689, 1377, and 1273 in the previous list are rejected for the
orbital calculations but are used with nine others for radiants, heights, and
miscellaneous data. The mean apparent relative velocity v for the eleven meteors
is 60-01 ±0-23 km ./sec. compared with 59-85 km./sec. from the preliminary data
in Table 97 (p. 284). The *no atmosphere’ velocity V = 60-44±0-21 km./sec.,
the geocentric velocity v g = 59-30±0-21 km./sec., and the heliocentric velocity
V = 41-29±0-17 km./sec.
The mean orbital elements are as follows:
SI <o i q l/ a
138-l°±0-5 161-2°±0-7 113-7°±0-3 0-951 ±0-003 a.u. 0-048±0-016(a.u.)“ 1
The correspondence of these elements with thoso of Comet 1862 III is even closer
than the preliminary data quoted in Table 99 (p. 287).
Measurements of the radiant position made in Czechoslovakia in 1947 and 1948
have boon given by Ceplecha.f The results of combined photographic and visual
measurements in 1952 have been published by Paroubek, SaSky, and Voz&rovA.J
Extensive discussions of the Perseid stream have been given by Guigay§ and
by Ahnert-Rohlfs.il From observations in the U.S.S.R. Astapovichtt concluded
that an easterly branch of the Poreeid stream existed, about 7° south in declina¬
tion and 10° west in right asconsion from the main radiant. This branch was
found to be active from 1926 August 6 to August 15 and its association with
Comet 1870 I was suggested. Miss Wright and Whipple were unable to find any
indication of this stream in the Harvard analysis referred to above.
CHAPTER XV
1. The Orionid shower
The 1953 radio-echo data for addition to Table 100 is as follows:
1953 Oct. 23 © 209-4 deg. Hourly rate > 6.
2. The Taurid shower
For comparison with § 2 (6), p. 297, the maximum rates during the Taurid
epoch observed with the radio-echo equipment in the years 1951-3 are as follows:
G deg.
Hourly rate
1951 Nov. 7
223-7
25
1952 Nov. 7
224-5
16
1953 Nov. 8
226-2
8
3. The Geminid shower
The following radio-echo observations made at Jodrell Bank during the 1953
Geminid shower are given for comparison with Tables 113, 117, and Fig. 153 (a).
t Coplecha, Z., Bull. Cent. Astr. Inst. Czech. 3 (1952), 95.
% Paroubek, A., SaSky, R., and VozArova, M., ibid. 6 (1953),144.
§ Guigay, G., J. des Observaleurs, 31 (1948), No. 1.
|| Ahnert-Rohlfs, E., Veroff. der Stcmwartc in Sonneberg, 2 (1952), No. 1.
tf Astapovich, I., Bull. Obs. Corp. Astr.-Godet. Soc. U.S.S.R. No. 19 (1933).
442
APPENDIX II
Solar longitude
©
Radiant
Hourly
rale
Date
ct
8
1953
Dec. 8
deg.
255-6
deg.
110
deg.
+ 30
12
1953
Dec. 9
256-7
110
33
22
1953
Dec. 10
257-7
112
33
26
1953
Dec. 11
258-7
111
33
20
1953
Dec. 12
259-7
113
34
57
1953
Dec. 13
260-7
113
33
71
1953
Dec. 14
261-7
115
30
61
CHAPTER XVI
The Giacobinid shower
A8 described on p. 331, an intense Giacobinid shower was observed during the
afternoon of 1952 October 9 when the earth crossed the orbit 195 days ahead of
the comet. From the history of the activity given in Table 125 it seemed possible
that when the earth crossed the orbit 170 days behind the comet on 1953 October
9 a meteoric storm might occur. Extensive preparations were made for this event
but the results were entirely negative, the rate of Giacobinid meteors being zero.
The reasons for this are not yet clear, but since a great shower was observed in
1933 when the earth crossed the orbit 80 days after the comet, it seems likely
that perturbations may have removed the debris further from the earth's orbit.
CHAPTER XVIII
The day-time meteor streams
The radio-echo observations, on p. 443, made at Jodrell Bank during the summer
of 1953 are given for comparison with Tables 148 and 150.
CHAPTER XIX
1. Visual determinations of the frequency distribution of the shower meteors
The results of an investigation made in Czechoslovakia of the frequency distri¬
bution in the 1952 Perseid shower have been given by KresAk and VozArovA.f
For meteors down to third apparent magnitude (zenithal magnitude +4) they
find the base x in equation (1), p. 384, to be 2-85. This is to be compared with
the value of 2-5 for the same magnitude range obtained by Opik (p. 384). Between
zenithal magnitudes +4 to +6 KresAk and VozArovA find that the number
remains approximately constant.
2. Radio-echo determinations of the frequency distribution
On p. 389 reference was made to a new radio-echo method for determining the
mass distribution. The method involved the measurement of the height distribu¬
tion and the full theory has been considered in two papers by KaiserJ and the
practical application has been described by Evans.§ A summary of the results
on the mass distribution of five major showers is given below. In all cases the
range of magnitudes was from +4 to +7 (zenithal).
f KresAk. L., and VozArovA, M., Buli. Cent. Aslr. Inst. Czech. 4 (1953), 139.
x Kaiser. T., Mon. Not. Roy. Astr. Soc. 114, No. 1.
§ Evans, S., ibid.
APPENDIX II
443
Date
Solar
longitude
O
Radiant position
Radiant
diam.
Hourly
rate
Shower
1953
a
s
o-Cetids
May 17
deg.
56 1
deg.
11
deg.
-2
deg.
3
8
Arietids
May 28
66-8
48
+ 24
3
11
29
67-7
39
18
3
16
30
68-7
48
23
3
13
31
69-6
48
34
6
21
June 2
71-5
43
29
3
24
3
72-5
38
28
3
31
4
73-4
43
25
3
40
6
74-4
41
16
4
53
6
75-3
46
27
3
40
7
763
44
16
4
64
8
77-3
44
25
3
54
9
78-2
47
24
3
43
10
79-2
47
17
3
67
11
80-1
45
25
4
50
12
81-1
48
24
3
37
13
820
45
30
3
33
14
830
46
24
4
17
15
83-9
46
24
3
20
16
84-9
52
25
3
23
{-Porseids
June 2
71 6
60
+ 26
3
16
3
72-5
57
29
5
24
4
735
63
25
6
34
6
74-5
60
25
4
30
6
75-4
62
24
3
34
7
76-4
60
17
3
33
8
77-3
62
23
7
29
9
78-3
69
24
3
20
10
79-2
66
17
7
31
11
80-2
65
17
11
26
12
811
68
28
7
26
13
82-1
68
25
10
30
14
83 1
72
24
12
19
15
84 0
63
20
5
23
16
850
67
17
8
13
/1-Taurids
June 28
964
82
+ 14
3
24
29
97-4
84
14
4
24
30
98-3
96
24
3
18
July 2
100-2
80
24
8
26
3
101-2
87
12
4
24
Quadrantids. Observed in 1953 and 1954, the Quadrantids show a normal
distribution of heights corresponding to an inverse power law of mass distribu¬
tion with an exponent p in equation (2), p. 384, of 1-68.
Day-time Arietids. Observed in 1952 and 1953 the Arietids are exceptional in
that the value of p in the mass law is considerably higher than the value for
sporadic meteors and is of the order of 2-5.
Day-time fl-Taurids. Apparently a normal shower in that the mass distribution
roughly obeys a power law with an exponent p = 1-75. Observed in 1953 only.
444
APPENDIX II
Perm* Notable visually for the large number of brilliant meteors, the Perseid*
are found to have the lowest value of p observed which is 1-66. The distribution
of heights is such that a moderate deviation from a power law may not produce
any considerable effect. Some cut off in the mass distribution must undoubtedlv
occur for the brightest meteors. Results obtained in 1952 and 1953 agree closelv
and no marked variation has been observed during the period of the shower.
Qemtnids. Observed in 1951 and 1952 the Geminids have normal distribution
of masses with p = 1-66 during the period December 9-12. The remainder of the
period, December 13-15, is characterized by a remarkable departure from a
power law distribution which takes the form of a strong concentration of meteors
m a range of magnitudes centred on +5. Fainter meteors appear to be consider¬
ably reduced in number.
CHAPTER XX
The Poynting-Robertson effect
Plavecf has discussed the influence of the Poynting-Robertson effect on close
pairs of meteors. He considers that meteor pairs may be originally binary systems
and shows that the Poynting-Robertson effect is the most important force
governing such systems. The dispersion of such pairs is shown to be very rapid
and hence the occurrence of true double meteors in the earth’s atmosphere is
likely to be very rare. Plavec also applies these ideas to the disintegration of a
meteor stream as a whole.
CHAPTER XXI
(а) The structure of the Peraeid meteor shower
The evolution of the Perseid shower was discussed on pp. 428-9. Further
reference to Hamid’s theory has been made by Miss Wright and Whipple,t who
compare the implications of the recent Harvard analysis with the predictions of
the theory.
A discussion of the structure of the Perseid shower has also been given in two
papers from Czechoslovakia.! It is concluded that no local accumulations exist
in the orbit up to a diameter of 100,000 km., except those due to random distribu¬
tion. Also, excluding the general decrease of density from the centre to the
borders of the stream, it is found that the distribution of meteors in the shower
is random. Application of the Poynting-Robertson effect indicates that the age
of the Perseid shower is about 10 7 years. This has to be compared with the age
°f 4X 10 4 years given by Hamid (p. 429) from considerations of perturbation
effects.
(б) The relation between minor planets and meteor streams
A brief discussion of the similarity between certain meteor showers and minor
planets has been given by Plavec.|| He concludes that there is no evidence that
the short-period showers and minor planets have a common origin, and suggests
that a general generical connexion between the two is more probable.
t Plavec, M., Bull. Cent. Aslr. Inst. Czech. 4 (1953), 60.
x Wright, F. W., and Whipple, F. L., Tech. Rep. Harv. Coll. Obs. No. 11 (1953)
(Harvard Reprint Series n—47).
§ KresAk, L., and VozArova, M., Bull. Cent. Astr. Inst. Czech. 4 (1963), 128, 139.
|| Plavec, M., ibid. 4 (1953), 195.
INDEX OF AUTHORS
Adams, J. C., 150, 337, 346,
347, 348.
Alcock, G. E. D., 4.
Alien, C. YV., 432.
Almond, M., 9, 48, 212,
230, 237, 246, 252, 255,
256, 257, 265, 267, 268,
269, 272, 273, 274, 275,
276, 285, 286, 287, 294,
312, 316, 317, 318, 320,
322, 324, 325.
Apploton, E. V., 23, 27,
329.
Arago, 259.
Army Operational Re¬
search Group, 28.
d’Arrest, 353.
Aspinall, A., 65, 112, 265.
Astapowitsch, 332.
Baade, W., 275.
Backhouse, T. W., 7, 8, 9.
Baker, J. G., 17, 18, 19.
Banwoll, C. J., 28, 29, 50,
329, 330, 358, 389.
Barnett, M. A. F., 23.
Bauer, C. A., 431.
Bauschinger, J., 94.
BoSvA*, A., 319, 320, 321,
322.
Bonzonberg, 3, 142, 259.
Bovorage, H. H., 28.
Bhar, J. N., 26.
Blum, 341.
BochnICek, Z., 322.
Boothroyd, S. L., 12, 14,
130, 131, 159, 163.
Bowen, E. G., 27.
Bradley, 349.
Brandes, 3, 142, 350.
Bredikhino, T., 278, 401,
425, 429.
Broit, G., 23.
Brorsen, 430.
Brouwer, D., 420.
Bullough, K., 265.
Borland, M. S., 16.
Carroll, P., 19.
Coplecha, Z., 9, 16, 284,
286, 287, 319, 320, 321,
322, 323, 324, 325.
Clegg, J. A., 43, 50, 55, 56,
61, 65, 76, 77, 220, 223,
225, 226, 228, 265, 320,
322, 329, 330, 358, 389,
390.
Closs, R. L., 45.
Cook, E. M., 4.
Corrigan, S. J., 353, 354.
Coulvior-Gravier, F. A., 97,
143, 144.
Cripps, F. R., 336.
Cromraelin, 327, 339.
Cunningham, L. F., 334.
Davidson, I. A., 390.
Davidson, M., 5, 92, 94, 97,
103, 191, 256, 259, 273,
326, 327, 334, 335, 414.
Davios, J. G., 9, 48. 67, 76,
78, 79, 212, 219, 230,
237, 246, 254, 316.
Donning, W. F., 3, 96, 97,
101, 102, 145, 154, 190,
249, 252, 259, 261, 266,
270, 271, 277, 278, 280,
281, 288, 290, 291, 292.
293, 297, 298, 299, 308,
310, 319, 326, 327, 340,
341, 350, 351, 352, 355,
357, 414, 415.
Dinwoodie, C., 336.
Dobson. G. M. B., 16, 198.
Dods, 332.
Dolo, R. M.. 265, 290, 350,
351, 355.
Downing, A. M. W., 346.
DzubAk, 321.
Eastman, 143.
Eastwood, E., 28.
Eckersloy, T. L., 23, 27.
Eddington, A. S., 166.
Elkin, W. J., 14, 15, 198,
352, 354.
Ellison, 332.
Ellyett, C. D., 67, 76, 78,
79, 254, 262, 263, 316.
Emanuelli, P., 328.
Evans, S., 389, 390.
Fedinsky, V. V., 16, 198.
Fishor, R. A., 134.
Fisher, W. J., 16, 142, 143,
145, 146, 147, 148, 149,
150, 198, 249, 250, 252,
263, 254, 256, 327, 343,
350.
Flaugergues, 350.
Forbos-Bentley, 332.
Gallo, J. G., 147, 154, 258,
263.
Ghose. B. N., 26.
Giacobini, 326, 335, 336,
413, 415, 428, 430.
Goodall, W. M., 23, 24, 27.
Groenhow, J. S., 46, 231.
Greg, R. P., 308.
Hamid, S., 401, 402, 420,
421, 429.
Hansel 1, C. W., 28.
Harang, L., 27.
Hardcastlo, J. A., 92.
Hargrave, D., 163, 164.
Hawkins, G. S., 65, 112,
231, 252, 255, 256, 257,
265, 268, 272, 285, 286,
287, 294, 312, 316, 317,
318, 320, 322, 324, 325.
Heis, 350, 352.
Heising, R. A., 23, 24
Herlofson, N., 76, 226, 230.
Herrick, E. C., 249, 259,
261, 277, 349, 350.
Herschol, A. S., 122, 154,
190, 252, 266, 286, 414.
Hey, J. S., 28,29,43,50,51,
62, 74, 75, 76, 329, 335,
358.
Hind, 353.
Hoffleit, D., 16, 21, 198,
200, 201, 203, 207, 282,
294, 344.
Hoflmeister, C., 1, 8, 9, 97,
103, 104, 105, 106, 107,
108, 118, 119, 122, 131,
132, 141, 142, 143, 144,
145, 146, 147, 149, 150,
152, 153, 246, 247, 249,
257, 264, 265, 266, 267,
269, 270, 272, 273, 274,
293, 294, 295, 297, 305,
308, 309, 311, 376, 424,
428.
Hogg, F. S., 343.
Hughes, V. A., 265, 320,
322, 358.
446
INDEX OF AUTHORS
Hulst, H. C. van de, 432,
433, 434.
Humboldt, 337, 339.
Huruhata, M., 342.
Huygens, 40.
Ingram, L. J., 27.
Ito, Y., 26.
Jacchia, L. G., 16, 21, 22,
205, 208, 209, 210, 257,
262, 282, 284, 295, 296.
315, 316, 329, 331, 333,
344, 386, 387.
Jones, L. F., 28.
Kaiser, T., 45, 389, 390.
King, A., 190, 280, 290,
308, 310. 311, 312, 328,
332, 334, 341, 342.
Kirkwood, D., 150, 256.
Kleiber, J. A., 146.
Klinkerfues, W., 349. 354.
Kopal, Z., 16, 329, 331,
333. 334, 386, 387.
Knabo, 133.
Knopf, 150, 151, 297, 503.
Krafft, 350.
Lane, J. H., 15.
Laplace, 94.
Larmor, J., 402, 403.
Lindblad, B. A., 271, 274,
275.
Lindemann, F. A., 16, 198.
Lovell, A. C. B., 9, 28, 29.
43, 48, 50, 76. 77, 97.
212, 230, 237, 246, 265,
320, 322, 329, 330, 358,
388, 389.
McCrosky, R. E., 19.
McIntosh, R. A., 264, 265,
266, 267, 269, 270, 271,
272, 273, 274, 275, 291,
295.
McKinley, D. W. R., 52,
53. 54. 73, 74, 75, 76. 82,
85, 132, 237, 238, 239,
240, 241, 242, 243, 244,
245. 246, 262, 263, 268,
273, 274, 284, 285, 316,
390.
Malzman, 332.
Maltzev, V. A., 145, 146,
147, 150, 310, 311, 312,
315, 317, 423.
Manning, L. A., 74, 76, 82,
284, 285.
Maria, H. B., 24.
Marsh, 308.
Mas term an, S., 252.
Mercer, K. A., 28.
Milligan, 332.
Millman, P. M., 16, 21, 52,
53, 54, 73, 74.75, 76, 132,
133, 135, 198, 200, 201,
203, 207, 262, 263, 282,
294, 329, 331, 333, 334,
344, 386. 387, 390.
Mindhara, T., 26.
Mitra, S. K., 26.
Montagne, 349.
Mourant, 332.
Nagaoko. H., 24.
Naisraith, R., 23. 27, 329.
Newton, H. A., 3, 86, 150,
259, 264. 270, 337, 345,
346, 350. 351, 352, 353.
NiessI.G. von, 103,141,142,
143, 144, 145, 146, 147,
149, 150, 151, 163, 428.
Nielsen, A. V., 92, 154.
Olivier, C. P., 1, 4, 12. 16,
86. 94. 96, 97, 188, 189,
198, 203, 247, 259, 264.
265, 267, 268. 269, 270,
276, 280, 290, 295, 315,
337, 339, 341, 350, 353,
355, 357, 425.
Olmsted, D., 3, 86, 337,
341.
Olmsted, M., 202, 253,
343.
Opik.E. J., 1,2, 6. 7, 9,10,
11, 12. 13. 106, 124, 128,
130, 131, 132, 136, 154,
155, 156. 157, 158, 159,
160, 161, 163, 164, 165.
166, 167, 169. 170, 171,
173, 175, 177, 178, 179,
181, 183, 184, 185, 186,
187, 188, 189, 193, 195,
196, 197, 201, 207, 210,
233, 234, 246, 247, 249,
277, 279, 280, 384, 385,
386, 410, 411, 431, 433,
434.
Pape, C. F., 258. 263.
Parsons, S. J., 74, 75, 76,
329, 335.
Peterson, A. M., 76, 82,
284, 285.
Peterson, H. O., 28.
Pickard, G. W., 26.
Piddington, J. H., 27.
Pierce, J. A., 27, 28, 60.
Plavec, M., 423, 424.
Pokrovsky, 257.
Pons, 349, 354.
Porter, J. G., 4, 5, 6, 12,
86, 94, 95, 154, 188, 189,
190, 191, 192, 193, 196,
196, 266, 273, 282, 294,
296, 302. 315, 328, 337,
344, 352, 356, 398, 414.
Poynting, J. H., 271, 402,
403, 405, 406, 407, 408,
409, 410, 412, 431, 434.
Prentice, J. P. M., 1, 4, 12,
28, 29, 96, 103,110,111,
188, 189, 190, 250, 261,
252, 253, 260, 262, 273,
280, 281, 282, 288, 289,
290. 291, 292, 293, 294,
319. 320, 322, 327, 328,
331, 332, 350, 362, 354,
358.
Prior, 143.
Qu&ck, E., 26.
Qu6telet, A., 249, 277, 360.
Raillard, 350.
Richter, N., 328, 384, 386,
386.
RigoUet, R., 261, 275.
Robertson, H. P., 271, 402,
403, 404, 405, 406, 407,
408, 409, 410, 412, 431,
434.
Roy, de F., 328, 329, 331,
332, 384, 385, 386.
Russell, H. N., 260.
Ryves, 332.
Sandig, H., 328, 384, 385,
386.
Schaeberle, 203.
Schafer, J. P., 23, 24, 27.
Schiaparelli, G. V., 3, 86,
94, 96, 99, 101, 102, 103,
110, 118, 120, 122, 277,
286. 287, 337, 345, 346,
347, 413, 425.
Schmidt, 96, 97.
Schulhof, 429.
Schwarzman, 332.
Shaine, 257.
Shapley, H., 12.
Skellett, A. M., 24, 27.
Smith, F. W., 356.
INDEX OF AUTHORS
447
Stanjukowitsch, K. P., 18,
198.
Stewart, G. S., 28, 29, 43,
60, 51, 62, 74, 75, 76,
329, 335, 358.
Stoney, G. H., 337, 340,
348.
Svoboda, J., 295.
Syara, P., 26.
Sytinskaja, H. N., 21, 332.
Taylor, A. H., 27.
Thomson, M. M., 16.
Torwuld Kohl, 143, 144.
Tumor, 202.
Tuvo, M. A., 23.
Twining, A. C., 3. 86, 280,
308, 337, 341.
Van^aok, V., 322.
Villard, O. G., 70. 82, 284,
285.
Walracsloy, 332.
VVartmann, 249.
Waters, H. H., 16.
Watson, F., 4, 14, 123, 124,
125, 129, 130, 131, 132,
135, 136, 137, 138, 139,
151. 152, 153, 274, 328,
351, 384, 385. 380.
Watson-Watt, R. A.. 27.
Webb, 350.
Weiss, E., 258, 263, 353.
Wells, R. C.. 19.
Wenz, W., 256.
Whipple, F. L., 1,2, 16, 17,
19. 20,104, 202.203, 204,
205, 200, 207, 209, 210,
211, 240, 241, 256, 257,
281, 282, 284, 286, 287,
297, 298, 299, 300, 301,
302, 303, 304, 306, 307,
308, 311, 312, 313, 315,
310, 317, 318, 377, 382,
383, 401, 405, 406, 407,
408, 409, 412, 415, 410,
418. 419, 420, 421, 422,
423, 425. 426, 427, 428,
429, 430, 431.
Whitney, W. T., 10.
Wilkins, A. F., 27.
Williams, J. D., 133, 134,
135.
Wilson. F., 252.
Wilson, R., 103, 164, 183.
Winnecke, 354.
Wolf, C., 96, 97.
Wright, F. W., 297, 298,
299, 300, 301, 302, 303,
304, 307, 343, 344, 346,
421.
Wyatt, S. P., 405, 406, 407,
408, 409, 431.
Wylie, C. C., 150, 329, 330,
331.
Yogi, 38, 39, 41, 67.
Yamamoto, A. S., 408.
Yarkovsky, 410, 411, 412.
Young, L. C., 27.
Zonker, 15.
Zeziolo, 350, 352.
INDEX OF SUBJECTS
References in italics are to pages on which figures are given, while those with an asterisk
are to pages on which the information is contained in tables
aberration, diurnal, 92-93.
accordance, defined, 190.
accordances: duplicate, reduction of, 191—
3; multiple, reduction of, 191-2.
aerial arrays, 37-39.
— coverage, 222 .
— power gain, see power gain.
— system: collecting area, defined, 56,
effective, 56, of Jodrell Bank equipment,
227*. and radiation pattern of aerial, 56;
elevation of, for measuring velocity,
212 ; electronic switching of, 41; of
Jodrell Bank, 67, PI. ii, 212-13, 227*;
used in observation, 35-41, 67; for
measuring velocity, 212-13.
aerials: directional characteristics, 222;
lobes, side, 36-39, effoct of, 235; radia¬
tion pattern of, and collecting area of
aerial system, 56; reciprocity theorem
and, 36; sensitivity contours of, 58.
— typos: broadside arrays, 38-39.
-dipole, half-wave, 39, 237, contro-
fed, 36-37.
-narrow-beam: for measuring velocity
of sporadic meteors, 212-37; collecting
area of, 223-8.
-single directional: summer day-time
streams investigated by, 359-63, their
radiants determined by, 368, their velo¬
cities measured by, 372, 374.
-wide-boam: for measuring velocity
of sporadic moteors, 237-46.
ago of showers, 397.
AI patrol camera, 17, 202, 209, 210.
amplitude variation-time methods for
measuring meteor velocity, 73, 76-85.
— variations of scattered echoes, 78-79.
Andromeda moteors, movement in orbit of
Biela's comet, 363-4.
angular velocity: calculation of, 155, 156;
correction to rocking mirror method,
156*; correlation between height and,
164; distribution of, 105-6; measure¬
ment of, 12, by use of rotating shutters,
14; observed waves and, 182; reduction
to zenithal angular velocity, 182 ; of
shower meteors, 184.
-zenit hal: angular velocity reduced to,
182; relation between height and, 157*.
‘anomalies’, 87, 88.
ant apex: defined, 213; experiments, 213,
223, 228, 230, 232, 234.
Anteros, 430*.
apex: defined, 213; experiments, 213, 223,
228, 230, 232, 233-4, 235, 237.
Apollo, 423, 430*.
apparent density of radiants, working
formula for, 171.
— velocity of meteor, defined, 90.
8-Aquarid shower, 270-5; activity, 270-1;
classification, 249*; cometary associa¬
tion, 275, 422; geocentric velocity, 273;
heliocentric volocity, 273; hourly rates,
270-1; shower length, 428*; orbit, 274-5,
276*, 380, elements of, 275*; origin,
424; radiants, 52, 272-3; radiant co¬
ordinates, 272", 440; radiant positions,
440; time of occurrence, 249*, 270;
velocities, 273-4.
-(1952), 274.
ij-Aquarid shower, 175, 263-9, 288, 295-6,
358; activity, 264-5, 359, 366* ; broadth
of stream, 265; classification, 249*;
comet associated with, 264, 269, 413*,
414, 415*, 422; hourly rates, 263-4,
265* ; shower length, 428* ; orbit, 268-9,
oloments, 267*, 269; periodicity, 269;
radiants, 265-6; radiant coordinates,
266*, 370*, 371*; radiant position, 370*,
371*; time of occurrence, 249*, 263, 265;
velocities, 266-8.
aroa of visibility, effective, for moteors of
different magnitudes, 129*.
argument of perihelion, defined, 87.
Aries, radiants in, see Arietid (night-time)
shower.
Arietid (night-time) shower, 275, 296-308;
activity, 297-8; geocentric velocity,
303; heliocentric velocity, 303; hourly
rates, 297, 367; orbit, 303-8, elements,
304*; origin, 421; radiants, 298-301;
radiant position, 300-1; velocities,
302-3.
a-Ariotid shower, 299; radiants, 298*.
8-Arietid shower, 413*.
c-Arietid shower, 299; radiants, 298*.
{-Arietid shower, radiants, 298*.
o-Arietid shower, radiants, 298*, 299.
northern Arietid shower, 299.
southern Arietid shower, 299, 300, 302*;
origin, 421.
Arietid summer day-time stream, 359,443;
activity, 363, 366*, 443*; classification,
359; cometary association, 422*; mass
brought into earth’s atmosphere by, 394;
orbit, 378,379*, 380, density and mass of
INDEX OF SUBJECTS
440
particles in, 395*, elements, 379*;
origin, 424; radiant coordinates, 370*.
371*; radiant positions, 370*, 371*;
velocities, 373*, 374-5, 377*.
Arizona expedition, 1, 7, 130, 152, 155;
meteor streaming observed by, 171;
velocity measurements by, 163-81, of
Opik and of Boothroyd, 159-63, Opik’a
analysis compared with Porter’s British
analysis, 195-7; visual techniques of,
10-14.
arrays, aerial, 37-39, 67.
‘artificial meteors’, 9, 104.
asteroids: orbits, 430*; Anteros, 430*;
Apollo, 423, 430*; Eros, 423; 1937 UB,
430*.
astronomical notation, 436.
astronomy, meteor, beginnings of scientific
intorest in, 337.
— radio, techniques, 1.
atmosphero, earth's: mass, meteoric, on-
toring, 135-8, 390-4; mass and energy
brought into, by sporadic meteors, 138*;
paths of meteor showors in, 248; velocity
of Porseids afiected by, 282.
— upper, meteor heights and, 2.
atmospheric absorption, offect on magni¬
tude of, 6.
attention, coefficient of, 8.
attraction, earth's, and moteors, 90, 142,
175.
0-Aurigid stroam: activity, 367*; geocen¬
tric velocity, 372; holiocentric velocity,
372; orbit, 377; radiant coordinates,
370*; radiant position, 370*; velocity,
377*.
beam, aorial: direction of, for measuring
velocity, 213; shape, range-time re¬
lationship of radio echoes and, 66;
width, and radiant position, 52.
beat frequency for continuous wave
method, 32; and range accuracy, 35.
Befivaf’s stroam, 319-25.
Bielid (Andromedid) shower, 288, 326,
349-54; activity, 349-51; classification,
249*; comet associated with, 349, 353-4,
413*, 414, 415*; hourly rate, 350*, 351;
shower length, 351, 428*; orbit, 353-4,
olements, 354*; periodicity, 351; radi¬
ants, 351; radiant coordinates, 351*; time
of occurrence, 249*. 351; velocities, 351-3.
Boltzmann’s constant, 47.
Boothroyd, Arizona results of, 159-63.
British meteor data on velocity of sporadic
meteors, Porter’s analysis, 190-7.
Cambridge, Mass., 17, 202, 209.
3595.60 G g
cameras: AI patrol, 17, 202, 209, 210;
copying, 19; double camera technique,
14, 202-11, 439; FA patrol, 17, 202, 209,
210; used in Harvard techniques, 16-20;
KA, 209; KB, 209; Ross Xpres, 17, 20*;
rotating shutter, 14, 16, 17, 19-20,
measurement of velocity by, 198;
Schmidt, 14, 20*; super Schmidt, 17,
18-20, 18, 20*. 210-11.
o-Capricomid stream, 270.
cathode-ray tube in radio-echo observa¬
tion. 30, 31, 41-43.
Cauchy's approximations for Fresnel
integrals, 80.
o-Cetid stream: activity, 366*, 443*;
cometary association, 422*; orbit, 377-
8 , elements, 379*; origin, 424; radiant
coordinates, 370*, 371*; radiant posi-
tions, 370*. 371*; velocity, 374, 377*.
Clegg method of measuring moteor radi¬
ants, 55-73.
coefficients: attention, 8; perception, 8.
collecting area of aerial system, 56, 227*;
dofined, 56; offect of eloctron donsity
on, 226; limits of, 69; and mass of
meteor, relationship botwoon, 57-58;
power gain, 44, 49.
-of narrow-beam aerials, 223-8.
-of an observor, estimation of, 9, 10*.
-for telescopic observations, 124.
colour correction for photometric magni¬
tudes, 22.
cometary index, variation of, 121, 122.
comets: meteor showers associated with,
413-24, set also separate showers and
streams; moteor showers having no
association with, 414, 415*; meteor
streams formed from, 424-9; meteoric
material ejected from, 401-2; orbits,
430*, identification with orbits of meteor
streams, 413-14; Whipple’s modol,
425-8, 429.
comets:
Biela (1852 III), 257, 349, 350, 353*,
354, 413*. 415*. 428*. 430*.
Blanpain (1819 iv), 415*.
Brorscn I, 430*.
d’Arrest, 426.
Denning (1881 v), 415*.
Encke, 297, 306, 307, 308, 318-19, 383,
413*, 415-21, 426, 428*. 430*; per¬
turbations for, 416*.
Finlay, 415*.
Giacobini-Zinner, 335, 336*, 413*, 415*,
428, 430*.
Grigg-Mellish (1907 II), 415*.
Grigg-Skjellerup, 415*, 430*.
460
INDEX OF SUBJECTS
COMETS ( corxt .):
Halley, 264, 268, 269, 288, 296, 296, 408,
*13*, 416*, 422, 428*; estimated mass
of, 426.
Kozik-Peltier (1939a), 257, 413*, 422,
Lexell (1770 I), 415*. [439.
Mellish (1917 I), 415*.
Pons-Winnecke, 349, 354, 413*, 415*.
Schwassmann-Wachmann, 415*.
Temple, ate 1866 I.
Tuttle: I, 439; (1926 iv), 415*; (1939k),
324, 413*.
Wolf, 426.
1680, 423.
1743 I, 415*.
1860 I, 257.
1861 I, 269, 260, 263, 413*, 415», 428*;
orbital elements, 263*.
1862 HI, 277, 286, 287, 413, 413*, 415*,
428*, 428-9.
1866 I (Temple), 337. 346, 347*, 400,
413, 413*, 415*, 428"; orbit, 347*.
1870 I, 441.
1900 III, 326, 327, 331.
1933 III, 428*.
1948 n, 275.
components, moteor: directly moving.
119; ocliptical, 104. 106; hyperbolic,
103, 119. 210, 213, 246; interstellar, 104,
424; meteor, sporadic, origin of, 246;
solar, 210 ; velocity, transverse helio¬
centric, 183*.
computation of orbit: of a metoor, 54, 94-
95; of meteor streams, 248.
constants: Boltzmann's, 47; gravitational,
89, 91, 141, 398.
continuous-wave technique for observing
diffraction pattern, 79-85; for measuring
velocity, 32, 35, 82-85, 237-46.
-with frequency modulated for
radio observation, 31-32.
-diffraction technique, velocity of
Gerainids determined by, 316-17.
corrections for: deceleration, 240-1; diur¬
nal motion, 240; lens distortion, 202;
photometric measurements of magni¬
tude, 21-22; velocity, angular, in rock¬
ing mirror method, 156*; zenithal attrac¬
tion, 240-1.
cosmological relationships of meteors,
413-34.
counting of meteors, 7-10.
critical aspect effect of meteor trails, 50.
cross-bearings for observing paths, 191.
cross-section for scattering, formula for, 43.
curve-fitting method of measuring meteor
velocity, 76.
Cygnid stream, 270.
daily frequency of sporadic meteors, 131,
132.
data, reduction of, for photographic plates.
20 - 22 .
debris, dispersion of, 397-412.
deceleration: correction for, 240-1; effect
of, 234; measurement of, 73, 75, 76.
December Ursids, ate under Ursids.
declination, effect of, 171.
— of radiant, determination of, 63, 65
67-68.
density: electron, 225; conversion to
visual magnitudes, 230-2; effect on
collecting area, 226.
— distribution of meteors, von Nieesl's
expression for, 103; relation between
height and, 203, 204.
— of particles in orbits of shower meteors,
394-6.
— of radiants: apparent, working formula,
171; surface, 169.
— spaco, per magnitude group, 384.
detector, type of, and signal obtained, 80.
determination: of doclination of radiants,
63, 65, 67-68; of radiant coordinates,
63-65; of right ascension of radiants, 63.
differential refraction, 202.
diffraction from a lino source, radio-echo
production in terms of, 73.
— pattern: continuous wave technique for
observing, 79-85; Frosnel, 237; of
radiants. 438; of reflected wovee, 78-79;
of trail, PI. iii.
— photographs, use of, to estimate errors
in velocity measurements, 214.
— thoory, and radio echoes, 74, 76.
diffusion, equation for, 166.
dipoles: centre-fed half wave, 36-37; half
wave, aerial, 39, 237; power gain ex¬
pressed in terms of, 44; Hertzian, 36,37.
directivity, 36. 38, 39.
directly moving component, 119.
-meteors, 118.
dispersion, theory of, 397; observational
error and velocity, 184; maximum-
error, 185.
dispersive effects in meteor streams, 397-
412.
display system of radio-echo observation,
41-43.
distribution: frequency, see under fre¬
quency ; mass, see under mass; of pro¬
jection ratios, 173, 174*; space, ate
under space; true, equation for, 166; of
velocities, angular, 105-6, geocentric
tangential, 168*, heliocentrio, 176-9,
180*, 181*, 234; space, 173-5, 175*-6*,
Opik's calculations, 167-81.
INDEX OF SUBJECTS
451
diurnal aberration, 92-93.
— distribution of sporadic moteore, 96-
122, 97; Hoffmeister’s investigations,
103-8, 107, 119; compared with Schia¬
parelli’s thoory, 101-2, 103.
— motion, corrections for, 240.
— rotation of tho earth, effect of, 112.
— variation in meteor rates, 8-9, 28.
-of mean hourly rates of radio echoes,
61.
Dona Ana, 17, 209.
Dopplor method: ‘fast Doppler', 85; ‘slow
Dopplor', 82-85; velocity of Perseids
moasured by, 284-5.
Doppler whistle, 74; defined, 80 n.
doublo-camora technique, 14, 202-11, 439;
Jacchia’s analysis of data, 208-9; velo¬
city distribution determined by, of
Gominida, 315*, of Lyrids. 262, of
Orionids, 296, of Perseids, 282, 284.
double-count method, 7-8.
doublo station technique, velocities of
Leonids determined by, 346*.
Draconid moteor showers, ate Giacobinid
shower.
drag, tangontial, 402.
duplicate observation, 3.
duration: formula for. 183; of shower
meteors, 184.
E region: offoct of moteore on, 23, 24-28;
olcctron density of, 23, 26.
oarth: atinosphoro of, volocity of meteor
in, 90-91, energy and moss brought into,
by sporadic meteors, 138*; attraction
of, and meteors, 90, 142, 175; attractive
force of, 398; diurnal rotation, offect of,
112 ; mean distribution of sporadic
motoors round, 118 ; modulation of
sporadic orbit round orbit of, 121, 122;
number of meteors falling to, 225;
orbital volocity of, 176; perturbations
duo to, 423*.
ecliptic latitude, distribution of sporadic
motoors in, 110.
ocliptical component, 104, 106, 424.
— meteors, 108.
ejection of meteoric material, 401-2;
radius, 428; velocity, 401, 429.
electron density of E region, 23, 26.
-of meteors, 225; conversion to visual
magnitudes, 230-2.
-in metoor trail, 44-46, 57; effect on
collecting area, 226.
— line density, 388.
electronic switching of aerial systems, 41.
elongation of the radiant: height and. 193;
height, velocity, and, 193-5; velocity
and, 195, 196; volocity, geocentric, and,
213.
— of true radiant, 93-94.
energy brought into earth's atmosphere by
sporadic meteors, 138*.
equations of meteoric motion, 86-95.
Eros, 423.
evaporation of meteors, 2, 136; rate, 389.
FA patrol camera, 17, 202, 209, 210.
‘fast Doppler’ mothod, 85.
fatigue, offect of, 105.
field correction for magnitude obtained by
photometric measurement, 22.
fireballs: day-tirao moteors observed as,
307; defined, 142; duration. 147; heights
of appoarance anil disappearance, 146,
147; holiocentric velocity, 146*; hypor-
bolic volocity, 142, 143, 148; path
lengths. 148. 148, 149; poriodicity of,
143. 144; radiants. 143, 145; apparent
radiants, 150, 151 ,152 ; concentration of
radiant*, 153; true radiant, 151. From
Draco radiant (1926). 327-8. 332; of
1933, 334.
— catalogue, von Niessl-Hoffmeister, 142—
54.
Fraunhofer component, 432, 433.
frequency: of different magnitudes, 129-
30; of moteore, Williams’s analysis, 133-
5; of projection ratios, 167-73.
— daily, of sporadic meteors, 131, 132.
— distribution of moteore, 130-5, 384-90,
442-3; radio-ocho techniques and, 135,
388-90. Of Geminid (1946), 389; Giaco¬
binid (1933), 386*. (1946), 386-8. 389;
Leonid (1933), 386; Porseid. 386; Quad-
rantids (1947), 389; of showor moteore
by visual observation, 384-8.
Fresnol diffraction pattern, 237.
— integral, 45, 77; Cauchy’s approxima¬
tions for, 80 .
— zones, 49, 79. 214, 438; oscillations, 35;
pattern, 48, 388.
galactic noise, 47, 48.
Geminid shower, 147, 148, 189, 202, 237,
308-19, 444; activity, 308-10, 441-2;
classification, 249*; comotary associa¬
tion, 422*, 422-3; heliocontric velocity,
316; hourly rate, 308-10, 363, 441-2;
showor length, 428*; life of, 424; orbit,
308, 317-19. 422-4, density and mass
of particles in, 395*. olomonts, 317*;
origin, 423, 424; particlo sizes, separa¬
tion of, 409; radiant, 310-14; radiant
coordinates, 311*. 312*, 313; radiant
position, 310-14; time of occurrence
INDEX OF SUBJECTS
462
249*. 308; velocity, 238-43, 316-17,
distribution, 240.
Gominid shower (1946): frequency distri¬
bution, 389; magnitude, 387*, 388».
-(1947), 63.
-(1949), 69, 214, 220; velocity dis¬
tribution, 218.
-(1960), 69.
(1963), orbit determined by radio¬
echo technique, 438.
A-Geminids: activity, 367*; radiant co¬
ordinates, 370* ; radiant position, 370*.
v-Gerainids: activity, 367*; radiant co¬
ordinates, 370*; radiant position, 370 # .
geocentric velocity of meteor. 142, 145,
241; calculation of, 220-2; defined, 90;
standard deviation, 255; relation be¬
tween elongation of meteor radiant and,
213; formula, 221; relationship with
solar longitude, 302-3; relation between
zenithal magnitude and, 180 *. 8-
Aquarids, 273; Arietid. 303; 0-Aurigid,
372; Bielids, 352; Leonids, 344; 54-
Poreeids, 372; Quadrantids, 256, 439;
Taurids, 303; see also separate showers
and streams.
-parabolic, 273.
— tangential velocities, distribution of,
168*.
Giacobinid (Draconid) showor, 288,326-37;
activity, 327-32; age, 397; classification,
249*; comot associated with, 326, 332,
335-7, 413*, 414,415*; hourly rate, 327,
328, 330, 331; shower length, 328. 428* ;
magnitude, 328; orbit, 335-7, density
and mass of particles in, 395; particle
sizes, separation of, 409; radiants, 332-
4; radiant coordinates, 326, 332, 334;
radiant position, 327, 332; recorded in
day-time by radio-echo technique, 326,
327, 331; time of occurrence, 249*;
velocity, 326, 334-5.
-(1933): frequency distribution, 386;
magnitude, 384-5.
-(1946), 16. 29, 74. 76; frequency
distribution, 386-8, 389; shower length,
329; magnitude, 387*, 388*; mass
brought into earth’s atmosphere by, 394.
-(1952), 331,442.
gnomic projection, effect on Great Circle
by, 19.
gravitational constants, 141, 398; for
velocity of meteor in its orbit, 89, 91.
Groat Circle, effect of gnomic projection
on, 19.
Harvard collection of photographic plates,
14, 143,299,311.
Harvard techniques for meteor photo¬
graphy, 16-22, 198-211, 440-1.
height of fireballs, 146, 147.
— meteor, 3; correlation between angular
velocity and, 164; in upper atmosphere
measurements, 2; data, source of, 3;
relation between density and, 203, 204 •
determination of, 202-3; ionization
varying with, 226 ; of hyperbolio
meteors, 197; meteor, showor, average,
193, 194*; meteor, sporadic, average,
193, 194*; observation of, 10-12;
radiant, elongation, and, 193; and radio¬
echo range, 61; relation between velo¬
city and, 2, 194*; relation between
velocity, elongation, and, 193-5; rela¬
tion between zenithal angular velocity
and, 157*.
— mean, shower meteors, 195; sporadic
meteors, 195; use of, 155, 166.
heliocentric velocity of fireballs, 146*.
heliocentric velocity, 104, 106, 141, 142,
316; relation between concentration of
meteors and, 234; dofined, 90; distribu¬
tion of, 175-9, 180*, 181*. 234. Arietid,
303; 0-Aurigid, 372; Leonid, 344; 64-
Perseid, 372; Taurid, 303; see also
separate showers and streams.
-parabolic, 234.
-projected, distribution of, 159-62.
— space velocities for sporadic motoors,
187.
— tangential velocity, relation botween
zenithal magnitude and, 188*.
Herschol’8 determination of radiant co¬
ordinates of Perseid shower, 286.
Hertzian dipole, 36, 37.
Hoy and Stewart method of measuring
meteor radiants, 50-52.
HofHeit’s and Millman's photographic
measurements of velocity, 198-201.
Hoffmeister’s investigation of diurnal
variation, 103-8, 107, 119, 247.
— von Niessl-, fireball catalogue, 142-64.
hyperbolic meteor component, 103, 119,
210, 213, 246.
— shape of radio echo, 54, 73, 75, 76.
— stream in Taurus, 146, 150.
— velocity of fireballs, 142, 143, 148.
-of meteors, 103, 108, 118, 130, 196,
201, 207, 209, 210, 233, 246, 247.
Icarus, minor planet 1566, 275.
infra visual meteors, 11, 13.
intensity of reflected wave, formula for, 78.
intensity-modulated range-time display,
42, 73, 82, 85; radio echo photographed
on, PI. i; trace, 82.
INDEX OF SUBJECTS
453
interplanetary particles, velocity of, and
formation of meteors, 433.
interstellar clouds, velocity of, 141.
— component, 104, 424.
— origin of sporadic meteors, 141.
— particles of matter: masses of, 139;
radii of, 139; velocity of, in solar system,
141.
— space, density of matter in, 139.
— streams, 143, 146, 150.
ionization: by meteors, 23, 24-28, 25 , 230,
245; at head of a meteor, 74, 438;
according to height of raoteor, 226 ; and
rotum of radio ocho, 73.
Jacohia’a analysis of double-camera data,
208-9.
Jodroll Bank Experimental Station:
radiant survey apparatus at, 65-73. 66 ,
PI. ii; radio-echo techniques for measur¬
ing volocity of sporadic meteors, 212-37.
Giacobinids, observation of, 329; 5-
Aquarid velocities measured by, 273-4;
Porsoid velocities measured by, 285-6.
Investigation of summer day-time
stroams at, 358-83.
Jupiter: attractive force, 397; orbit of,
porturbations due to, 308; perturba¬
tions due to. 346, 354. 356,397,398,400,
416, 423, 429; swooping action of. 434.
Locortid stream, 270.
Ions distortion, correction for, 202.
Leonid shower. 147, 148, 175, 288, 337-48;
activity, 338-40; classification, 249*;
comet associated with, 337, 346, 400,
413, 413*. 414. 415*, 428*; frequency
distribution of, 386; goocontric velocity,
344; heliocentric velocity, 344; hourly
rates, 338, 339*. 340 1 orbit. 346-8.
Schiaparelli's determination of, 337,
345-6; poriodicity, 337, 338; radiants,
340-4, path of, 345 ; radiant coordinates,
341, 342*, 343; radiant position, 341,
342*; time of occurrence, 249*; veloci¬
ties, 344-5, 346*.
-(1833), 3, 4, 86.
-(1931), 24.
-(1932), 16, 24, 26.
-(1933), 16; frequency distribution
of, 386.
-(1940), 27.
longitude of perihelion, 87.
— solar, relationship with geocentric
velocity, 302-3.
— distribution of sporadic meteors, 110,
120.
luminosity: distribution in Perseid shower.
384. 385*; magnitude error and, 193;
relation between mass, velocity, and,
136; relation between meteors seen and,
7; relation between volocity and, 108,
179-81, 187, 210; and zonithal magni¬
tude, 6.
Lyrid shower. 147, 175, 258-63; activity,
259-61; age, 400; classification, 249*;
comet associated with, 259, 260, 263,
413*, 414, 415*; hourly rate, 259-60;
shower length, 428'; orbit. 263, elo-
ments, 263; periodicity, 259; radiants,
261-2; radiant coordinates, 261, 440*;
radiant position, 259, 262, 439; time of
occurrence, 249*. 259; velocities, 262-3.
-(1922), 260-1.
-(1946), 29.
McKinley's measurement of meteor velo¬
cities, 237-46.
— and Millman's method for measuring
meteor radiants, 52-55.
magnitude: atmospheric absorption and,
6; estimate of, from comparing visual
and radio-echo rates, 231-3; observer's
Hold and, 7; field of vision as a funotion
of, 8; frequency of difloront, 129-30;
proportional to logarithm of intensity,
135; relation botwoon lino density and,
46; mass to be attributed to a given,
136. and, 137 ; measurement of, uso of
photometry for, 21-22; numbor of
moteors of given, calculation of, 232;
relation botweon chango of numbor and,
384; and numbor of meteors obsorvod,
123; observed, correction to zonithal,
131 ; range of, 230-3, relationship bo¬
twoon power gain and, 49; effect on
volocity distribution of, 237; visual,
conversion of cloctron density to, 230-2;
zonithal, dofined, 6, relation botwoon
. geocentric velocity and, 180*, relation
between heliocentric tangential volocity
and, 188*. and luminosity, 6. Giaco*
binid, 328, (1933), 384-5. (1946), 387*.
388*.
— correction, 6-7, 6*. scale, 128.
— error, and luminosity, 193.
magnitude function, 8.
— group, space density por, 384.
— scales, correlation of nakod eye and
telescopic observations, 128*.
magnitudes, stellar, 6.
map plotting of observed paths, 3, 4, 190.
Mare: attractive forco, 398; orbit of,
Taurids and, 307; porturbations, 423.
mass, meteoric: in earth’s atmosphere,
135-8,390-4; magnitude and, 136, 137 • ;
454
INDEX OF SUBJECTS
in meteor streams, 425; relationship
between velocity, luminosity, and, 136.
mass of Perseid meteors of second magni¬
tude, 136.
— of particles in orbits of shower meteors,
394-6.
mass distribution of meteors, 135-8;
determined by Kaiser and Evans, 389-
90; relationship between echoes recorded
and, 49.
showor meteors, number and,
384—96.
matter, density of, in intorstellar space. 139 .
— meteoric, density of, in solar system.
1 oJ.
moan heights, use of, 155, 156.
Mercury: attractive force. 398; orbit of.
Taurids and, 307.
metooric mass entering earth's atmosphere
135-8, 390-4.
material: ejection from comets of, 401 -
2; total mass of, in orbits, 425.
-ejectod, 401-2; radius, 428; velocity.
401, 429. 7
motion, fundamental equations, 85-95.
moteorites, 2, 138, 154; micro-, 2; Pul.
tusk, 154.
motoor(s): activity, variation in, 391 ;
'artificial', 9, 104; close-pairs of, 444;
components, see under components;
cosmological relationships of, 413-34;
counting of, 7-10; donsity distribution
of. von Niessl’s expression for, 103;
directly moving, 118; ecliptical, 108;
effect on E region by, 23, 24-28, 25;
earth's attraction and, 90, 142, 175;
evaporation, see evaporation; formation
of, volocity of interplanetary particles
and, 433; heights, see heights; hyper¬
bolic, frequency, 180*. height of, 197;
and ionization. 23, 24-28, 25, 74, 230,
245; densely ionizing, 73, 74, 82, 224 n.;
infra visual. 11, 13; of given magnitude,
observed, calculation of, 232, see also
magnitude; mass, relationship between
collecting area and, 57-58, see also mass;
number of, falling to earth, 225, relation¬
ship botween radio echo and visual
totals, 358; hourly number of, relation
between radio echo rates and, 223; true
number of, falling on a square kilometre,
232; observation of, by radio techniques,
1, 30-49; observation, probability of, of
different classes of, 125-6; orbit, see
orbit; path length, see path length;
photography of, see photography;
physics, 2; radiants, see radiants; cor¬
respondence between radio echoes and,
28-30; radio waves propagated by, 24-
28 ; rates, see rates; streaming observed
in Arizona expedition, 171; structure of,
444; zodiacal light and, 432-4; velocity,
see velocity.
— showers of: age of, 397; classed as
summer day-time streams, 359,366*-7* •
comets associated with, 413-24; having
no associations with comets, 421-4
422*; frequency distribution deter¬
mined by radio echo, 388-90; major,
248-383; naming of, 248, 249*; occur¬
rence of, 248; orbits of, computation,
248, mass and density of particlos in,
394-5; origin of, 401; particles in, dis-
appearance of, 390; paths of, 248;
radiant position of, defined, 248; see also
the various named showers.
— streams of: daylight, l, see also summer
day-timo streams; dispersive effects in,
397-412; formation of, 401, 424-9^
Schiaparelli on, 425; intensity, 172*1
lost, 349-57; total mass of meteorio
material in, 425; orbit, computation of,
86-95, identification with orbits of
comets. 413-14; periodic, 326-48; por-
manent, definod, 248, (January to July)
248-69, (July to August) 270-87, (Sop-
tember to Decomber) 288-325; pers¬
pective and, 56; planetary origin of
some, 424; and minor planets, 444;
width of, 402; see also the various named
streams.
METEORS, SHOWERS AND STREAMS
5-Aquarid showor, 270-5; activity, 270-
1; classification, 249*; cometary
association, 275, 422; geocentric
velocity, 273; heliocentric velocity,
273; hourly rates, 270-1; shower
length. 428*; orbit, 274-5, 276*, 380,
elements of, 275*; origin, 424; radi¬
ants, 52, 272-3; radiant coordinates,
272*. 440; radiant positions, 440;
time of occurrence, 249*, 270; veloci¬
ties, 273-4. (1952), 274.
ij-Aquarid shower, 175, 268-9, 288,
295-6,358,359, 366*; activity, 264-6,
359, 366*; breadth of stream, 265;
classification, 249*; comet associated
with, 264, 269, 413*, 414, 415*, 422;
hourly rates, 263-4, 265*; shower
length, 428*; orbit, 268-9, elements,
267*, 269; periodicity, 269; radiants,
265-6; radiant coordinates, 266*,
370*, 371*; radiant position, 370*,
371*; time of occurrence, 249*, 263,
265; velocities, 266-8.
INDEX OF SUBJECTS
465
Arietid (night-time) shower, 275, 296-
308; activity, 297-8; geocentric
velocity, 303; holiocentric velocity,
303; hourly rates, 297, 367; orbit,
303-8, elements, 304*; origin, 421;
radiant positions, 300-1; velocities,
302-3.
a-Arietid shower, 299; radiants, 298*.
8-Arietid shower, 413*.
«-Arietid showor, 299; radiants, 298*.
{-Arietid shower, radiants, 298*.
e-Ariotid shower, radiants, 298*, 299.
northorn Ariotid shower, 299.
southern Ariotid showor, 299, 300, 302* ;
origin, 421.
Arietid summer day-time stroam, 359,
443; activity, 363, 366*, 443*; classi¬
fication, 359; cometary association,
422* ; mass brought into oarth’s atmo¬
sphere by, 394; orbit, 378. 379*, 380,
donsity and mass of particles in, 395*,
oloments, 379*; origin, 424; radiant
coordinates, 370*, 371*; radiant
positions, 370*. 371* ; velocities, 373*,
374-5, 377*.
0-Aurigid stream: activity, 367*; geo-
contric volocity, 372; holiocentric
volocity, 372; orbit, 377; radiant
coordinates, 370*; radiant positions,
370*; volocity, 377*.
Boivuf’s 8troum, see Ursids, Docombor.
Bielid (Andromedid) showor, 288, 326,
349-54; activity, 349-51; classifica¬
tion, 249*; comot associated with,
349, 353-4, 413*, 414, 415*; hourly
rato, 350*. 351; showor length. 351,
428* ; orbit, 353-4, olemonts of, 354* ;
periodicity, 351; radiants. 351; radiant
coordinates, 351*; time of occurrence,
249*, 351; velocities, 351-3.
a-Capricornid stroam, 270.
o-Cotid stream: activity, 366*, 443*;
comotary association, 422*; orbit,
377-8, olemonts, 379*; origin, 424;
radiant coordinates, 370*, 371*;
radiant positions, 370*. 371*; velo¬
city, 374, 377*.
Cygnid stream, 270.
Geminid shower, 147, 148, 189, 202, 237,
308-19, 444; activity, 308-10, 441-2;
classification, 249*; comotary associa¬
tion, 422*, 422-3; holiocentric velo¬
city, 316; hourly rate, 308-10, 363,
441-2; shower length, 428* ; lifo, 424;
orbit, 308, 317-19, 422-4, density and
mass of particles in, 395*. elements,
317*; origin, 423, 424; particle sizes,
separation of, 409; radiant, 310-14;
radiant coordinates, 311*, 312* ; 313;
radiant position, 310-14; timo of
occurrence, 249*, 308; velocity, 238-
43, 315-17, distribution, 240. (1946):
frequency distribution, 389; mag¬
nitude, 387*. 388*. (1947), 53.
(1949), 69, 214, 220; velocity dis¬
tribution, 218. (1950), 69. (1953),
orbit determined by radio-echo tech¬
nique, 438.
A-Cominid stroam: activity, 367*;
radiant coordinates, 370*; radiant
position, 370*.
► Geminid stream: activity, 367*; radi¬
ant coordinates, 370*; radiant posi-
tion, 370*.
Giocobinid (Draconid) showor, 288, 326-
37; activity, 327-32; ago, 397; classi-
fication, 249* ; comot associated with,
326. 332. 335-7. 413*. 414. 415*;
hourly rate. 327, 328, 330, 331; showor
longth. 328, 428*; magnitudo, 328;
orbit, 335-7. donsity and moss of
particles in, 395; particle size, separa¬
tion of, 409; radiants, 332-4; radiant
coordinates. 326. 332, 334; radiant
position, 327, 332; recorded in day-
timo by radio-echo, 326, 327, 331;
timo of occurronco, 249*; volocity,
326. 334-5. (1933): frequency dis-
tribution, 386; magnitude, 384-5.
(1946), 16. 29, 74. 76; frequency dis-
tribution, 386-8, 389; showor length,
329; magnitudo, 387*, 388*; mass
brought into earth's atmosphere by,
394. (1952), 331, 442.
Lacortid stream, 270.
Leonid shower, 147, 148, 175, 288, 337-
48; activity, 338-40; classification,
249* ; comet associated with, 337, 346,
400, 413, 413*. 414, 415*. 428*; fre¬
quency distribution, 386; goocentric
velocity. 344; holiocentric velocity,
344; hourly rates, 338, 339*, 340;
orbit, 345-8, Schiaparelli's deter¬
mination of, 337, 345-6; periodicity,
337, 338; radiants, 340-4, path of.
345; radiant coordinates, 341, 342*,
343; radiant position, 341, 342* ; timo
of occurrence, 249*; velocities, 344-5,
346*. (1833), 3, 4, 86. (1931), 24.
(1932), 16. 24, 26. (1933), 16; fre¬
quency of, 386. (1940), 27.
Lyrid showor, 147,175,258-63; activity,
259-61; age, 400; classification, 249* ;
comot associated with, 259, 260, 263,
413*, 414, 415*; hourly rate, 259-60;
shower length, 428*; orbit, 263,
456
INDEX OF SUBJECTS
METEORS, SHOWERS AND STREAMS (con<.):
elements, 263; periodicity, 259; radi¬
ants, 261-2; radiant coordinates, 261 ,
440*; radiant position, 259, 262, 439;’
time of occurrence, 249*. 259; veloci¬
ties, 262-3. (1922), 260-1. (1946), 29.
Onomd shower, 147, 148, 189, 288-96;
activity, 288-90, 441; classification,
249"; comet associated with, 269,
288, 290-6, 408, 422; hourly rate, 288,
289, 290*; shower length, 428*; orbit,
^95-6; position, 291; radiants, 290-4;
radiant coordinates, 290, 291, 293,
294; radiant position, 291; time of
occurrence, 249*, 288; velocities.
^94-5.
a-Orionid stream: activity, 367*; radi¬
ant coordinates. 370*; radiant posi¬
tion, 370*.
Perseid shower, 147, 148. 175, 231, 237.
275-87, 444; activity, 277-8; age,
397, 400; classification, 249*; comet
associated with, 277, 286, 413, 413*
414, 415*, 428*, 428-9, 441; fre-
quency distribution. 386; heliocentric
velocity, 286; hourly rates, 275, 277,
278, 279\ 367; life, 276, 278; lumino-
sity distribution, 384, 385*; orbit,
28ft “ 7 » 401, density and mass of par¬
ticles in, 395*. Schiaparelli'8 compu¬
tation of, 277, 286, elements, 287*,
441; origin of, 420-9. 444; periodicity,
278; radiants, 4. 278, 280-2, 286,
dispersion of, 402; radiant coordi-
nates, 280*. 281, Herschel’s deter¬
mination of, 286; radiant position,
278, 280-2, 440, 441; structure of,
444; time of occurrence, 249*, 276,
277, 278; velocities, 281, 282-6.
(1920), 8. (1921), 8. (1946), 29.
(1947), 96.
-ofsecond magnitude, mass of, 136.
54-Perseid stream: activity, 367"; goo-
centric velocity, 372; heliocentric
velocity, 372; orbit, 377; radiant
coordinates, 370*; radiant position,
370*; velocity, 377*.
C-Porseid stream: activity, 363, 366*-7*.
443*; classification, 359; comet as¬
sociated with, 413*; mass brought
into earths atmosphere by, 394;
orbit, 382, density and mass of par¬
ticles in, 395*. elements, 381*;
origin, 421; radiant coordinates, 370*,
371*-2*; radiant positions, 370*,
371 *-2*; velocity, 373*. 374. 376,
377*.
Piscid stream: activity, 366*; radiant
coordinates, 370-, 371*; radiant
positions, 370*, 371*.
-Piacid stream: activity, 368*; radiant
coordinates, 370*; radiant positions,
Pons-Winnecke, 364-7; activity, 366-
classification, 249*; comet associated
w.th, 413*, 414, 416*; hourly rate,
355; orbit, 366-7, elements, 357* ;
perturbations due to Jupiter, 357*’
400, 401; radiants, 355-6; radiant
coordinates, 355*; radiant position,
355 ; tune of occurrence, 249*, 355 •
velocities, 356-7.
Quadrantid shower, 147, 249-58, 443-
activity, 249-52; classification, 249*;
cometary association, 257, 413*, 422*.
439; geocentric velocity, 256, 439-
heliocentric velocity, 255, 256, 257-
hourly rate, 250-2; shower length’.
428*; orbit, 256-8, density and mass
of particlos in, 395*. elements, 267*;
parabolic elements, 266; periodicity’,
252; position, 249; radiants, 252-4;
radiant coordinates, 254*. 439!
radiant position, 263; timo of ocour!
ronce, 249; velocities, 254-6. (1946),
29. (1947), frequency distribution,
389«
shower: angular velocity, 184 ; classifi-
cation, 248; durations of, 184; fre¬
quency distribution, 384-90, 442-3-
height, 193, 194*, moan, 196; number
and mass distribution of, 384-96;
times of fall into sun, 408*.
solar: frequency, 180*.
sporadic: activity, seasonal variation of,
120-2. average, 193, 194*; com¬
ponent, origin of, 246; distribution of,
49, in ecliptic latitude, 110, 120,
major showers and, 96, Prentice’s
investigations, 108-11, radio-echo
investigations of, 112-17; distribu¬
tion, diurnal, 96-122, 97, compared
with Schiaparelli’s theory, 101-2, 103,
Hoffmeister’s investigations of, 103-8,
107, 119; distribution, mean, round
the earth, 118 ; distribution, seasonal,
96-122, 97, compared with Schia¬
parelli’s theory, 102-3, 120; distribu¬
tion, true, 117-19, 185; diurnal
variation, 112-14; daily mass of, 137;
daily frequency, 131, 132; heights,
mean, 195; mass distribution, 9, 123—
40; mass and energy brought into
earth’s atmosphere by, 138; number
of, 9, 123-40; orbit of, 247, 429, 430*,
distribution of, 438-9, modulation of,
INDEX OF SUBJECTS
467
around earth’s orbit, 121, 122; origin,
1, 141, 163. 207, 210, 246-7, 429-32;
space distribution of, 138-40; volocity
of, 141-247, British data on, 190-7,
Opik’s measurements of, 165-89,
photographic measurements of, 198-
211, radio-echo techniques for measur¬
ing, 212-46; velocity distribution, 2,49,
119, double-camera investigation of,
439; velocity, holiocentric space, 187 .
spaco, distribution of, 186*.
summer day-time streams, 118,122, 238,
297, 326, 358-83; activity, 359-68,
443*; classification, 249*; observed
as fireballs, 307; hourly rates, 363,
364-5 ; orbits, 378-83; radiants, 368-
72; radiant coordinates. 370*-2*;
radiant positions, 368, 369, 370*-2*;
revealed by radio echoes, 248, 307,
358-9; showers classed as, 359, 366*-
7* ; times of occurrence, 249* ; veloci-
ties, 372-6. (1947). 65. 71.
_Stream B: radiant coordinates,
370* ; radiant positions, 370*.
-Stream C': radiant coordinates,
370*; radiant position. 370*.
Tourid showor, 202, 205, 296-308;
activity, 297-8; ago, 420, 421; clas¬
sification, 249*; comet associated
with, 297, 307-8, 413*, 415-21; geo-
contric velocity, 303; holiocentric
volocity, 303; hourly rate, 297, 367,
441; shower longth, 428* ; orbit, 303-
8, 377, and orbits of Morcury, Venus,
and Mors, 307, oloments, 304*;
origin, 305, 421; radiants, 298-301;
radiant coordinates, 298*, 299*;
radiant position, 300-1; timo of
occurrence, 249*, 296-7; velocities,
302-3.
/J-Taurid stream, 207, 444; activity,
367*. 443*; classification, 359; comet
associated with, 413*, 415-21; orbit,
382-3, density and mass of particles
in, 395*, elements, 381* ; origin, 421;
radiants, 298*, 377; radiant coordi¬
nates, 370*-l *; radiant positions. 370*,
372*; velocities, 373*. 374, 376, 377*.
y-Taurid stream, radiant, 298*.
c-Taurid stream, radiant, 298*.
£-Taurid stream, radiant, 298*.
K-Taurid stream, radiant, 298*.
A-Taurid, 299; radiant, 298*.
northern Taurid stream, 299, 302*, 307.
s-(southern) Taurid stream, 299, 300,
301, 302*.
^-Taurid stream, radiant, 298*.
Ursid stream, December (Becvars
stream), 319-25; activity, 319-21;
classification, 249*; comet associated
with, 324-5, 413*, 414, 415*; hourly
rate, 319-21, 323; orbit, 323-5,
elements, 324*; radiant, 321-2;
radiant coordinates, 321*, 322*;
radiant position, 321, 322*; time of
occurrence, 249*, 320; velocities, 323.
micro-meteorites, 2.
Milky Way, The, galactic noise from, 48.
Millman and Hoffloit’s photographic
measurements of velocity, 198-201.
— and McKinley's method for measuring
meteor radiants, 52-55.
modulation frequency caused by Fresnel
zone oscillations, 35.
Neptune, attractive force of, 398.
von Niessl’s expression for density dis¬
tribution of meteors, 103.
von Niessl-Hoffmeister fireball catalogue,
142-54.
nodes of orbit: defined, 86-87; offoct of
perturbations on. 399.
noiso, relation of, to detection of raotoor
ocho, 47.
— galactic, 47, 48.
— rocoivor, 46-48.
notation: astronomical, miscellaneous,
436; miscellaneous, 437; radio, 436-7.
number: chango of, relation botwoon
magnitude and, 384; and moss dis¬
tribution of showor meteors, 384-96;
of meteors observed, magnitude and, 123.
Nyquist's theorem, 46-47.
Oak Ridgo, 17, 202, 209.
observation: duplicate, 3-4; photographic
techniques, 14-22, 198-211, 212; radar
tochniques for, 32; radio-echo tech¬
niques for, 23-49, 67, 212-46; reticulo
method for, 10 - 12 , 188; rocking mirror
method for, 106; telescopic, 123-40,
applied to Giocobinids, 328, Booth-
royd’8 method, 159-63; visual tech¬
niques, 3-14, 141-97, 212; of Arizona
expedition, 10-14.
observational error dispersion: Opik's
corrections for, 166-7; and velocity, 184.
occulted trail, first photograph of, 15.
Opik, work of, 155-89; analysis of Arizona
data of, compared with Porter’s British
analysis by, 195-7; calculation of dis¬
tribution of space velocities by, 167-81;
correction for observational error dis¬
persion by, 166-7.
optical diffraction theory and electron
density in meteor trail, 44-46.
458
INDEX OF
orbits, comets: identification with orbits of
meteors, 413-14.
— meteor: ‘anomalies’, 87, 88; computa¬
tion of, 64, 94-96; determination by tri¬
angulation. 73, 70; elements of, 80-87,
ate oho separate showers and streams,
symbols, 435-0; retrograde motion
defined, 80; nodes defined, 80-87; plane
of, 87; radio-echo measurement of, 258,
209, 317, 318, 438; velocity of meteor in
its, 88-90.
— sporadic moteors, 247; comparison with
those of asteroids and comots, 430 *;
distribution of, 430-9.
moteor streams: computation of, 248 ;
identification with orbits of comets,
413—14.
— spatial, computation of, 80-95.
Orionid shower, 147, 148, 189, 288-90;
activity, 288-90, 441; classification,
249*; comot associated with, 209, 288,
295-0, 408, 422; hourly rate, 288, 289,
290* ; showor longth, 428*; orbit, 295-0;
position, 291; radiants, 290-4; radiant
coordinates, 290, 291, 293, 294; radiant
position, 291; time of occurrence, 249*,
288; velocities, 294-5.
a-Orionid stronm: activity, 307*; radiant
coordinates, 370*; radiant position,
370*.
Palomar, Mount, 14.
parabolic regression method of measuring
meteor volocity, 75.
— volocity, 108, 141, 208, 323; Schia-
parolli's equation, 99.
— constants for volocity of moteor in its
orbit, 89.
— limiting volocity of moteor in its orbit,
90.
— limit, 119; and telescopic observation,
130.
— goocontric velocity, 273.
— heliocentric volocity, 234.
paraboloidal aerial, 39-40.
parallactic displacement, 3.
particlos, meteoric: in moteor showers,
disappearance of, 390; mass and density
of, in orbits of meteor showers, 394-6;
equations of motion of, 403; effect of
radiation pressure on, 410-11; separa¬
tion of, according to size, 403, 409; rate
of fall into sun, 402, 405, 450*; time of
fall into sun, 431; in space, velocity of,
141; velocity, 427.
path, moteor: data on, accuracy of, 4;
determination by wand or extended
string, 4, 190, from segmented trails, 20;
SUBJECTS
map-plotting of, 3, 4, 190; and number
of meteors observed, 123; observation
of, 10-12; perturbations and, 90.
— of meteor showers, 248.
path length, meteor: source of data on 3 •
for different magnitudes, 129*.
-of fireballs, 148, 148, 149.
perception, coefficient of, 8.
perihelion: argument of, defined, 87 ;
longitude of, 87.
periodic phenomenon, idea of, 80.
— streams of meteors, 320-48.
periodicity: comet, Pons-Winnecke, 354;
fireballs, 143, 144; of moteore, see
separate showers and streams.
Pereeid showor, 147, 148, 175, 231, 237.
275-87, 444; activity, 277-8; ago, 397,
400; classification, 249*; comet associ¬
ated with, 277, 280, 413, 413*, 414, 416*,
428*. 428-9,441; frequency distribution,
380; heliocentric velocity, 280; hourly
rates, 275, 277, 278, 279*. 307; lifo, 270,
278; luminosity distribution, 384, 385*;
orbit, 280-7, 401, donsity and mass of
particles in, 396*, Schiaparelli’s com-
putation of, 277, 280, olomonts, 287*,
441; origin, 428-9, 444; periodicity, 278;
radiants, 4. 278, 280-2, 280, disper-
sion of, 402; radiant coordinates, 280*.
281, Herechel’s determination, 280;
radiant position, 278, 280-2, 440, 441;
structure of, 444; time of occurrence,
249-, 270, 277, 278; velocities, 281,
282-6.
-of second magnitude, mass of, 130.
54-Pereeid stream: activity, 367*; goo¬
contric velocity, 372; heliocentric volo¬
city, 372; orbit, 377; radiant coordi-
nates, 370*; radiant position, 370*;
velocity, 377*.
(-Pereeid stream: activity, 363, 366*-7*,
443*; classification, 359; comet asso¬
ciated with, 413*; mass brought into
earth’s atmosphere by, 394; orbit, 382,
density and mass of particles in, 395*,
elements, 381*; origin, 421; radiant
coordinates, 370*. 371*—2*; radiant
positions, 370*, 371 *-2*; velocity, 373*,
374, 376. 377*.
-(1920), 8.
-(1921), 8.
-(1946), 29.
-(1947), 96.
perspective, and meteor streams, 50.
perturbations: calculation of, 398-401;
constants, 419*; effect of, 399; funda¬
mental equations, 417-19; and paths of
meteors, 96. Due to Jupiter, 346, 364,
INDEX OF SUBJECTS
459
366, 397, 398, 400, 416, 423, 429; to
Mars, 423; to Saturn, 346, 397, 398, 429;
to sun, 401; to Vonus, 423.
photographic techniques of observation,
14-22, platos, data from, reduction of,
20 - 22 ; double camera, 202-11; fro-
quoncy distribution of shower meteors
doterminod by, 384-8; Harvard, 1, 16-
22, 143; volocity of sporadic meteors
measured by, 198-211, Millman and
Hoffloit's results, 198-201, Whipple’s
rosults, 202-8.
photometry: magnitude measured by, 21-
22; and meteor trails, 21.
piscid stream: activity, 366*; radiant co¬
ordinates, 370*, 371* ; radiant positions,
370*. 371*.
y-Piscid stream: activity, 366*; radiant
coordinates, 370*; radiant positions,
370*.
planots: motcors associated with, 307, 346;
origin of short-poriod moteor streams
from, 424; porturbotions due to, effect
of, 397-401.
— minor, relation of moteor streams and,
444.
plasma resonances, 45.
Poisson’s equation, 152.
polar diagrams of aerial systems, 36, 38,
40, 41, 61, 224.
Polar Yoar Expedition of 1932, 27.
Pons-Winnocko motoors, 354-7; activity,
355; classification, 249*; comet associ¬
ated with, 413*, 414, 415* ; hourly rate,
355; orbit, 356-7, olomonts, 357*;
porturbations duo to Jupiter, 357 *, 400,
401; radiants, 355-6; radiant coordi¬
nates, 355*; radiant position, 355*; time
of occurrence, 249*, 355; velocities,
356-7.
Porter’s analysis of British meteor data,
190-7; compared with Opik's, 195-7.
powor donsity, 36; flux of power formula,
36, 37; of scattered radiation, formula
for, 44.
— gain (G) of an aerial system, 36, 37, 40,
41, 48-49, 67, 212, 230; and collecting
area, 44, 49; oxprossod in terms of a
half-wave dipole, 44; and magnitude
rango, 49.
Poynting-Robortson effect, 271, 402-9,
431, 444.
Prentice’s investigation on distribution of
sporadic moteors, 108-11.
projection ratios: distribution, 173, 174*;
frequency of, 167-73; spread in, limits,
185, and velocity, 184.
pulse rate for radio observation, 30, 35.
pulse shape, relationship of band width to,
34.
— spectrum, 33.
— techniques: for observing diffraction
pattern, 78-79; for observation, 30-31,
31, 32, 33, 35; for reflection of radio
waves, 24, 27; for measuring velocity
of sporadic moteors, 212-37.
— width, 32-33, 35, 41; and range
accuracy, 48.
Pultusk meteorite, 154.
Quadrantid shower, 147, 249-58, 443;
activity, 249-52; classification, 249*;
cometary association, 257, 413*, 422,
439; geocontric volocity, 256, 439; helio¬
centric volocity, 255, 256, 257; hourly
rate, 250-2; showor length, 428* ; orbit,
256-8, donsity and mass of particles
in, 395*, olomonts, 257*; parabolic
eloraonts, 256; periodicity, 252; position,
249; radiants, 252-4; radiant coordi¬
nates, 254*, 439; radiant position, 253;
time of occurrence, 249; velocities,
254-6.
-(1946), 29.
-(1947), froquoncy distribution, 389.
radar, and meteor observation, 32.
radiant: calculation of, 220-2; corrections
to observod, 91-94; data on, source of,
3; doclination of, determination of, 63,
65, 67-68; dofined, 86; donsity, ap¬
parent, working formula, 171; surfoco,
169; determination of, 49, accuracy of,
4, error of, from reticule observations,
12; diffusoncss of, 70; elovation, defined,
52, and range distribution of echo, 52;
elongation of, relation between geo¬
centric velocity and, 213, relation be¬
tween hoight, velocity, and, 193-5;
errors, 191; measurement of, 1, 50-73,
Clegg method, 55-73, Hoy and Stewart
method, 50-52, McKinley and Millman’s
mothod, 52-55; variation in numbor
visible, Schiaparelli's theory, 96-101;
right ascension, determination of, 63;
survey apparatus at Jodrell Bank, 65-
73; zenith angle, relation between radio
meteor rates and, 241; see also separate
showers.
— apparent, 90; determination of, 110,
202; distribution, 117.
— space, 151, 152, 153.
— ’stationary’, 288, 290, 291, 292, 293.
— true, 93; elongation of, 93-94.
— coordinates: defined, 51 n.; determina¬
tion of, 63-65; visual observation of,
190; see also separate showers.
460
INDEX OF SUBJECTS
radiant position: aerial beam width and,
62; defined, 61, 248; determination of,
68; variation and range of echo rate and,
66 ; see also separate showers.
— of fireball, 143, 145 ; apparent, 160, 151,
152; concentration, 153; true, 151.
radiation, relation between retardation
and, 402-3.
— pattern of aerial and collecting area of
system, 56.
pressure: effect on a rotating particle
of, 410-11; from the sun, 138.
radiators: centre-fed half-wave dipole;
36-37; Hertzian dipole, 36, 37.
radio apparatus for the study of meteors,
30.
— astronomy, techniques, 1 .
— echo: amplitude, formula, 224; meteor
activity, variation in. determined by,
391, activity of Giacobinida observed by,
329, 330, 331; correspondence between
moteor and, 28-30; critical aspect of
trail, 50; duration of, 42, 46, short-
duration, 26, of short duration similar
to random noise impulses, 66; diffraction
theory and, 74, 76; diffraction tech¬
nique, velocities measured by, 254, 285,
372; frequency distribution determined
by, 135, 388-90, 442-3, fundamental
equations of, 43-49; hourly rates of,
mean, diurnal variation, 51; hourly
rates of moteors estimated by, 252*.
265*, 271, 277, 290*, 297, 308. 310\
339*; relationship between mass dis-
tribution and, 49, Kaiser and Evans
mothod to determine, 389-90; relation¬
ship betwoon number recordod and
wave-length, 49; relation to noise, 47;
observation by means of, 23-49; orbits
calculated from, 258, 269, 317, 318, 438;
photographs of, on an in tensity-modu¬
lated rango-time display, PI. i; pro¬
duction in terms of diffraction from
a line source, 73; meteor radiants
measured by, 56-73, Clegg method, 55-
73, Hoy and Stewart method, 56-52,
McKinley and Millman's method, 52-55;
relation between zenith anglo of radiant
and meteor rates, 241; radiant coordi¬
nates determined by, 254•, 262, 294,
312*, 313, 322; radiant positions ob¬
served by, 280*, 281; range of, 58-63,
limit, 225; rango distribution of, and
elevation of radiant, 52; range-time
curves, 61-63; range-time display and
shape of, 54; range-timo relationship of,
anil beam shape, 56; rate, 58-63, for¬
mula, 225-6, relation between hourly
number of meteors and, 223, variation
and range of, and radiant position, 66,
comparison with visual rate to estimate
magnitude, 231-3; relation between
receiver noise level and number of
echoes obtained, 46-48; shape of, 64
"3, 75, 76, defined, 64, hyperbolic, 64^
73, 75, 76; signal obtained dependent on
type of detector, 80; of sporadic dis-
tribution, 112-17; measure of strength,
47; summer day-time streams revoaled
by, 248, 307, 358-9; from head of trail,
438; transient, 27, 28, 43, 49; velocity
of meteors measured by, 73-86, 212-46
254, 263*. 268,273,274-, 284,285* 286
316, 323, 335*, 352.
-notation, 436-7.
-techniques for study of meteors, 30-
49; for measuring moteor velocities
73-85.
— waves: formula for intensity of reflected
wave, 78; frequencies, critical, 23, 25-
26 ; length, for radio-echo observation,
43-49, for measuring velocity, 212, and
echoes recorded, 49; propagation of,
meteors and, 24-28; reflection of, pulso
technique for, 23, 24, 27; scattering of,
236-1, into skip zone, 27.
range accuracy: and beat frequency, 36;
and rounding of pulso, 33; and pulse
width, 48; and receiver band width, 34,
35.
— measurement by pulso or frequency
modulated mothod, 32.
range-time curves of radio echoes, 61-63.
— display and shape of radio echo, 64.
-methods for measuring moteor
velocity, 73-76.
-plots: and determination of radiant
position, 68; showing velocity measure¬
ments, 375. Of Geminid showers (1949,
1950), 69, 70; of summer day-time
streams, 71.
-relationships of radio ochoes and
aerial beam shape, 66.
-trace of echoes. 82, 83, 84, PI. i.
rates, meteor: diurnal variation in, 8-9,
28; diurnal variation of sporadic, 115;
determined by radio echo, 231-3, rela¬
tion between zenith angle of radiant and,
241; visual, 9, 10*. 231-3.
receiver band width, and meteor observa¬
tion, 32-35, 47.
— noise, 46-48.
reciprocity theorem: and aerials, 36; and
magnitude, 205.
recording system of radio-echo observa¬
tion, 41-43.
INDEX OF SUBJECTS
461
recurrence frequencies, velocity determina¬
tion and, 48.
refraction, differential, 202.
retardation, relation between radiation
and, 402-3.
reticule method of observation, 10-12,
188 ; for recording trails, 181.
retrograde motion of orbit, defined, 86.
right asconsion of radiants, determination
of, 83.
rocking mirror method of measuring an¬
gular velocities, 12-14, 156; apparatus,
165; corrections to, 166*; frequency
moasured by, 182; used in Tartu, 181-9.
rotating-shuttor technique for measuring
velocity, 14, 16. 17, 19-20,198, 207, 282,
295, 333.
Saturn: attractive force, 397; perturba¬
tions duo to, 346, 397, 398, 429.
scottoring, 43-45; amplitude variation of,
78; cross-section formula, 43; diffrac¬
tion theory and, 74, 76; diffractional,
by zodiacal particles, 432; effects, ab¬
normal, 27-28; fundamental, formula,
67; by ionized motoor trail, 30; power
density formula, 44; of radio wave,
230-1, into skip zone, 27.
Schiaparelli: computation of orbit of tho
Loonids, 337, of Persoids, 277, 286;
on formation of meteor streams, 425;
equation of, for parabolic velocity, 99,
101 , 102 ; thoory of, for variation in
number of meteor radiants visible, 96-
101 , compared with observed diurnal
variation, 101-2, 103, compared with
observod seasonal variation, 102-3, 120.
Schmidt camera, 14, 20*; super, 17, 10-20,
18, 20*, 210-11.
Scorpius, streams in, 150, 151.
soasonal variation: of sporadic motcor
activity, 96-122, compared with Schia¬
parelli’s theory, 102-3, 120.
segmented trails, measurement of, 202.
showers of meteors, see under meteors,
skip zone, scattering of radio waves into, 27.
‘slow Doppler’ mothod, 82-85.
solar component of meteors, 210.
— longitude, relationship with geocentric
velocity, 302-3.
— system: density of meteoric matter in,
139; origin of, 397; origin of sporadic
meteors in, 207, 210; velocity of inter¬
stellar particles in, 141.
Soledad, 17, 20, 209, 211.
space density per magnitude group, 384.
— distribution of sporadic meteors, 1 38—
40.
space radiants, 151, 152, 153.
— velocities, 159, 173-5, 176*-6*, Opik’s
calculations, 167-81; for sporodio
meteors, 186 *; heliocentric, for sporadic
meteors, 187.
spatial orbit, see under orbit,
sporadic meteors, see under meteors,
‘stationary radiant’, 288, 290, 291, 292,
293.
Stewart and Hey method of measuring
meteor radiants, 50-52.
stream intensity, 172*.
streams of meteors, see under meteors,
string, extended, use of, for observing
path, 4, 190.
summer day-time streams, 118, 122, 238,
297, 326, 358-83; activity, 359-68,443* ;
classification, 249*; observed as fireballs,
307; hourly rates, 363, 364-5 ; orbits,
378-83; radiants, 368-72; radiant co¬
ordinates, 370*-2*; radiant positions,
368, 369, 370*-2*; revoalod by radio
echoes, 248, 307, 358-9; showers classed
as, 359, 366*-7*; times of occurrence,
249*; velocities, 372-6.
-Stream B: radiant coordinates,
370*; radiant positions, 370*.
-Stream C': radiant coordinates,
370*; radiant positions, 370*.
-(1947), 65, 71.
sun: attractive force, 397; porturbations
duo to, 401; radiation pressure of, 138;
rate of fall of a particle into, 402, 405,
406* ; times of fall of moteoric particles
into, 408*, 431.
surfoco density of radiants, 169.
symbols: orbital olomonts, 435-6; velocity,
435.
tangential drag, 402.
Tartu observations, 181-9.
Taurid showor, 202,205,296-308; activity,
297-8; age, 420, 421; classification,
249*; comet associated with, 297, 307-8,
413*, 415-21; geocentric velocity, 303;
heliocentric velocity, 303; hourly rate,
297, 367, 441; shower length, 428*;
orbit, 303-8, 377, and orbits of Mercury,
Venus, and Mars, 307, elements, 304*;
origin, 305, 421; radiants, 298, 301;
radiant coordinates, 298*, 299*; radiant
position, 300-1; time of occurrence, 249*,
296-7; velocities, 302-3.
/J-Taurid stream, 297, 443; activity, 367*,
443*; classification, 359; comet associ¬
ated with, 413*, 415-21; orbit, 382-3,
density and mass of particles in, 395*.
elements, 381*; origin, 421; radiants,
462
INDEX OF SUBJECTS
298", 377; radiant coordinates, 370*,
371*; radiant positions, 370*, 372*;
velocities, 373*, 374, 376, 377*.
y-Taurid stream, radiant, 298*.
«-Taurid stream, radiant, 298*.
{-Taurid stream, radiant, 298*.
K-Taurid stream, radiant, 298*.
A-Taurid stream, 299; radiant, 298*.
northern Taurid stream, 299, 302*, 307.
s-(southem) Taurid stream, 299, 300, 301,
302*.
{-Taurid stream, radiant, 298*.
Taurus, hyperbolic stream in, 146, 150.
telescopic observation, 123-40.
three-point method of measuring meteor
velocity, 76; of measuring velocity of
Perseids, 284.
timing orrora in visual techniques, 4 - 5 .
trails, meteor: critical aspect effect of, 50;
density of, and duration of echo, 46;
diffraction pattern of, PI. iii; electron
density in, 44-46, effective, 57; fixed
reticule for recording, 181 ; formation of,
modulation frequency caused by Fresnel
zone oscillations during, 35; head of,
radio echo from, 438; hoight of meteor
determined from, 202-3; occulted, first
photograph of, 15; photometry of, 21;
powor scattered from, and peak trans¬
mitter power, 48; scattering by ionized,
30; segmented, 20, 198, 202; specularly
reflecting properties of. 65, 213. Of
Giacobinid stream, 334; of Leonids, 343,
344; of Persoids, 281.
transient ochoes, 27, 28, 43, 49.
transmitter: for radio observation, 30, for
continuous wave techniques, 237; power
of, and radio observation, 35, and power
scattered from meteor trail, 48.
— band width, formula for, 33.
— pulse: rate, 212; width, 32-35, 41.
triangulation, determination of orbit of
meteor by, 73, 76.
Uranus, 346; attractive force of, 398.
Ursids, December (Be6v4f's stream), 319-
25; activity, 319-21; classification,
249*; comet associated with, 324-5,
413*. 414, 415*; hourly rate, 319-21,
323; orbit, 323-5, elements, 324*;
radiant, 321-2; radiant coordinates,
321*, 322*; radiant position, 321, 322*;
time of occurrence, 249*, 320; velocities,
323.
van de Hulst’s theory of zodiacal light,
432-4.
velocity, moteor: according to apex experi¬
ments, 233; apparent, defined, 90;
Arizona measurements, 183-81; data on,
source of, 3; defined, 86; determination
of, meteor height and, 2, and recurrence
frequencies, 48, from segmented trails,
20; deviation, mean standard, 218; dis¬
tribution, 2. 220, 242-6, calculation of,
228, effect of magnitude on, 237 ,
theoretical and experimental compared,
229-30; relation between elongation
and, 195, 196 ; relation between elonga¬
tion, height, and, 193-5; relation bo-
tween height and, 194*; -luminosity
relation, 108, 179-81. 187, 210; relation-
ship between luminosity, mass, and,
136; correction for magnitudes obtained
by photometric measurement, 22 ;
measurement of, 1 , by continuous wave
method, 32, 35, 82-85, by curve-fitting
method, 76, from diffraction photo¬
graphs, errors in, 214, by radio tech¬
niques, 73-86, by range x dR/dt method,
75, by rotating-shutter camora, 14, 16,
17, 19-20, 198, 207, 282, 295, 333, by
visual observation, 12-14; obsorvational
orror dispersion and, 184; probable,
233; spread in projection ratios and,
184; symbols, 435.
-angular: calculation of, 166, 156;
distribution of, 105-6; correlation be¬
tween hoight and, 164; measurement of,
by means of rotating shutters, 13-14,
correction to, 156*; observed waves and,
182; reduction to zenithal angular
velocity, 182.
-zenithal: angular velocity re¬
duced to, 182 ; relation between hoight
and. 157.
-geocentric, 142, 146, 241; calcula¬
tion of, 220-2; dofined, 90; forumla,
221 ; relation betweon elongation of
meteor radiant and, 213; relationship
with solar longitude, 302-3; relation
betweon zenithal magnitude and, 180*;
see also separate showers .
-parabolic, 273.
-tangential, distribution of, 168*.
-heliocentric, 104, 106, 141, 142, 210,
255, 256, 257,316; relation between con¬
centration and, 234; defined, 90; dis¬
tribution of, 175-9, 180*, 181*, 234; see
also separate showers.
-parabolic, 234.
-projected, distribution of, 169-
62.
-tangential, relation between zeni¬
thal magnitude and, 188*.
-transverse, components of, 183*
INDEX OF SUBJECTS
463
velocity, meteor, hyperbolic, 103, 108,
118, 130, 195, 196, 201, 207, 209, 210,
233, 246, 247.
-parabolic, 141, 268, 323; Schia¬
parelli's equation for, 99, 101, 102.
— of densely ionizing meteors, measure¬
ment of, 73, 74, 82.
— orbital, of earth, 175.
— of firoballs: compared with volocity of
moteors, 150*.
-holiocontric, 146*.
-hyperbolic, 142, 143.
— of interplanetary particles and forma¬
tion of meteors, 433.
— of interstellar clouds, 141.
— of intorstollar particlos in solar system,
141.
— of moteor: in earth’s atmosphere, 90-
91; in free fall, 142; in its orbit, 88-90;
compared with velocity of firoballs, 150V
— of meteoric particlos, 427; in space,
141.
— of meteors, sporadic, 141-247; British
data, 190-7; distribution, 49, 119,
doublo camera investigation of, 439;
moasuromont of, by photographic
mothods, 198-211, by radio-ocho tech¬
niques, 212-46; space distribution, 186*,
Opik’s calculations, 167-81, heliocentric,
159-61, 187.
— of showor motoors, angular, 184.
Venus: attractive force of, 398; orbit of,
and Taurids, 307; perturbations due to,
423.
visibility, area of, effective, for moteors of
different magnitudes, 129*.
vision, field of, difference in magnitude
and, 7; a function of magnitude, 8.
visual observation, see under observation.
— rates, compared with radio-echo rates
to estimate magnitude, 231-3.
wand, use of, for determining path, 4, 190.
Whipplo’s comet model, 425-8, 429.
— photographic measurements of velocity,
202 - 8 .
Yagi arrays, 38-39, 41, 67.
Yarkovsky effect, 410-11.
zonith attraction, 91-92, 104; correction
for, 240-1.
— angular volocity: angular velocity
reduced to, 182; height and, 157*.
— distance, 106.
— magnitude: dofined, 6; goocontric
velocity and, 180*; holiocontric tan-
gontial velocity and, 185*; and lumino¬
sity, 6.
zodiacal light: meteors and, 432-4; origin
of, 432.
— particles, 432-4.
53390
PRINTED IN
GREAT BRITAIN
AT THE
UNIVERSITY PRESS
OXFORD
BY
C HARL ES BATEY
PBINTEB
TO THE
UNIVERSITY
Live Music
Archive
Librivox
Free Audio
Metropolitan Museum
Cleveland
Museum of Art
Internet
Arcade
Console Living Room
Open Library
American
Libraries
TV News
Understanding
9/11